A survey of linear matrix inequality techniques in stability analysis of delay systems

References

• Boukas , E-K and Liu , Z-K . 2002 . Deterministic and Stochastic Time Delay Systems , Boston : Birkhäuser .
   Google Scholar
• Boukas , EK , Liu , ZK and Shi , P . 2002 . Delay-dependent Stability and Output Feedback Stabilisation of Markov Jump System with Time-delay . IEE Proceedings of Control Theory and Applications , 149 : 379 – 386 .
   Google Scholar
• Boyd , S , El Ghaoui , L , Feron , E and Balakrishnan , V . 1994 . “ Linear Matrix Inequalities in System and Control Theory ” . In in SIAM Studies in Applied Mathematics , Philadelphia, Pennsylvania : SIAM .
   Google Scholar
• Cao , Y-Y , Sun , Y-X and Cheng , C . 1998a . Delay-dependent Robust Stabilisation of Uncertain Systems Multiple State Delays . IEEE Transactions on Automatic Control , 43 : 1608 – 1612 .
   Web of Science ®Google Scholar
• Cao , Y-Y , Sun , Y-X and Lam , J . 1998b . Delay-dependent Robust H ∞ Control for Uncertain Systems with Time-varying Delays . IEE Proceedings of Control Theory and Applications , 145 : 338 – 344 .
   Google Scholar
• Chen , B , Lam , J and Xu , S . 2006 . Delay-dependent Stability Analysis and Control Synthesis of Fuzzy Dynamic Systems with Time Delay . Fuzzy Sets and Systems , 157 : 2224 – 2240 .
   Web of Science ®Google Scholar
• Chen , B and Liu , X . 2005 . Delay-dependent Robust H ∞ Control for T-S Fuzzy Systems with Time Delay . IEEE Transactions on Fuzzy Systems , 13 : 544 – 556 .
   Web of Science ®Google Scholar
• Chen , B , Liu , X and Tong , S . 2006 . Memory State Feedback Guaranteed Cost Control for Neutral Delay Systems . International Journal of Innovative Computing, Information and Control , 2 : 293 – 303 .
   Web of Science ®Google Scholar
• Chen , C , Feng , G and Guan , X . 2005 . Delay-dependent Stability Analysis and Controller Synthesis for Discrete-time T-S Fuzzy Systems with Time Delays . IEEE Transactions on Fuzzy Systems , 13 : 630 – 643 .
   Web of Science ®Google Scholar
• Chen , J and Latchman , HA . 1995 . Frequency Sweeping Tests for Stability Independent of Delay . IEEE Transactions on Automatic Control , 40 : 1640 – 1645 .
   Web of Science ®Google Scholar
• Chen , JD , Lien , CH , Fan , KK and Cheng , JS . 2000 . Delay-dependent Stability Criterion for Neutral Time-delay Systems . Electronics Letters , 36 : 1897 – 1898 .
   Web of Science ®Google Scholar
• Chen , W-H , Guan , Z-H and Lu , X . 2004 . Delay-dependent Output Feedback Stabilisation of Markovian Jump System with Time-delay . IEE Proceedings of Control Theory and Applications , 151 : 561 – 566 .
   Google Scholar
• Chen , W-H and Zheng , WX . 2007 . Delay-dependent Robust Stabilisation for Uncertain Neutral Systems with Distributed Delays . Automatica , 43 : 95 – 104 .
   Web of Science ®Google Scholar
• Cho , HJ and Park , JH . 2007 . Novel Delay-dependent Robust Stability Criterion of Delayed Cellular Neural Networks . Chaos, Solitons & Fractals , 32 : 1194 – 1200 .
   Web of Science ®Google Scholar
• Chu , T-G . 1997 . Analysis of Practical Stability and Lyapunov Stability of Linear Time-varying Neutral Delay Systems . International Journal of Systems Science , 28 : 919 – 924 .
   Web of Science ®Google Scholar
• Du , B , Lam , J and Shu , Z . 7–11 July 2008 . “ A Delay-partitioning Projection Approach to Stability Analysis of Neutral Systems ” . In in IFAC World Congress 2008 7–11 July , Seoul, Korea
   Google Scholar
• Du , B , Lam , J , Shu , Z and Wang , Z . “A Delay-partitioning Projection Approach to Stability Analysis of Continuous Systems with Multiple Delay Components,” . IET Control Theory and Applications , In Press
   Web of Science ®Google Scholar
• Dugard , L and Verriest , EI . 1998 . Stability and Control of Time-delay Systems , London : Springer-Verlag .
   Google Scholar
• Fridman , E . 2001 . New Lyapunov-Krasovskii Functionals for Stability of Linear Retarded and Neutral Type Systems . Systems & Control Letters , 43 : 309 – 319 .
   Web of Science ®Google Scholar
• Fridman , E . 2006 . Descriptor Discretised Lyapunov Functional Method: Analysis and Design . IEEE Transactions on Automatic Control , 51 : 890 – 897 .
   Web of Science ®Google Scholar
• Fridman , E , Pila , A and Shaked , U . 2003 . Regional Stabilisation and H ∞ Control of Time-delay Systems with Saturating Actuators . International Journal of Robust & Nonlinear Control , 13 : 885 – 907 .
   Web of Science ®Google Scholar
• Fridman , E , Seuret , A and Richard , J-P . 2004 . Robust Sampled-data Stabilisation of Linear Systems: an Input Delay Approach . Automatica , 40 : 1441 – 1446 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 2001a . New Bounded Real Lemma Representations for Time-delay Systems and Their Applications . IEEE Transactions on Automatic Control , 46 : 1973 – 1979 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 2001b . A New H ∞ Filter Design for Linear Time Delay Systems . IEEE Transactions on Signal Processing , 49 : 2839 – 2843 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 2002a . A Descriptor System Approach to H ∞ Control of Linear Time-delay Systems . IEEE Transactions on Automatic Control , 47 : 253 – 270 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 2002b . An Improved Stabilisation Method for Linear Time-delay Systems . IEEE Transactions on Automatic Control , 47 : 1931 – 1937 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 2002c . On Delay-dependent Passivity . IEEE Transactions on Automatic Control , 47 : 664 – 669 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 2003 . Delay-dependent Stability and H ∞ Control: Constant and Time-varying Delays . International Journal of Control , 76 : 48 – 60 .
   Web of Science ®Google Scholar
• Fridman , E , Shaked , U and Xie , L . 2003 . Robust H ∞ Filtering of Linear Systems with Time-varying Delay . IEEE Transactions on Automatic Control , 48 : 159 – 165 .
   Web of Science ®Google Scholar
• Gao , H and Chen , T . 2007 . New Results on Stability of Discrete-time Systems with Time-varying State Delay . IEEE Transactions on Automatic Control , 52 : 328 – 334 .
   Web of Science ®Google Scholar
• Gao , H , Lam , J , Wang , C and Wang , Y . 2004 . Delay-dependent Output-feedback Stabilisation of Discrete-time Systems with Time-varying State Delay . IEE Proceedings of Control Theory and Applications , 151 : 691 – 698 .
   Google Scholar
• Gao , H and Wang , C . 2003 . Comments and Further Results on ‘A Descriptor System Approach to H ∞ Control of Linear Time-delay Systems’ . IEEE Transactions on Automatic Control , 48 : 520 – 525 .
   Web of Science ®Google Scholar
• Gorecki , HS , Fuska , P , Grabowski , S and Korytowski , A . 1989 . Analysis and Synthesis of Time Delay Systems , New York : Wiley .
   Google Scholar
• Gouaisbaut , F and Peaucelle , D . July 5–7 2006a . “ Delay-dependent Robust Stability of Time Delay Systems ” . In The 5th IFAC Symposium on Robust Control Design July 5–7 , Toulouse, , France
   Google Scholar
• Gouaisbaut , F and Peaucelle , D . July 5–7 2006b . “ A Note on Stability of Time Delay Systems ” . In The 5th IFAC Symposium on Robust Control Design July 5–7 , Toulouse, , France
   Google Scholar
• Gu , K . 1997 . Discretized LMI Set in the Stability Problem of Linear Uncertain Time-delay Systems . International Journal of Control , 68 : 923 – 934 .
   Web of Science ®Google Scholar
• Gu , K . 1999a . Discretized Lyapunov Functional for Uncertain Systems with Multiple Time-delay . International Journal of Control , 72 : 1436 – 1445 .
   Web of Science ®Google Scholar
• Gu , K . 1999b . A Generalised Discretisation Scheme of Lyapunov Functional in the Stability Problem of Linear Uncertain Time-delay Systems . International Journal of Robust & Nonlinear Control , 9 : 1 – 14 .
   Web of Science ®Google Scholar
• Gu , K . 1999c . “ Partial Solution of LMI in Stability Problem of Time-delay Systems ” . In Proceedings of 38th IEEE Conference on Decision and Control 227 – 232 . Phoenix, , USA
   Google Scholar
• Gu , K . 2000 . “ An Integral Inequality in the Stability Problem of Time-delay Systems ” . In Proceedings of 39th IEEE Conference on Decision and Control 2805 – 2810 . Sydney, , Australia December
   Google Scholar
• Gu , K . 2001a . Discretization Schemes for Lyapunov-Krasovskii Functionals in Time-delay Systems . Kybernetika , 37 : 479 – 504 .
   Web of Science ®Google Scholar
• Gu , K . 2001b . A Further Refinement of Discretised Lyapunov Functional Method for the Stability of Time-delay Systems . International Journal of Control , 74 : 967 – 976 .
   Web of Science ®Google Scholar
• Gu , K . 2003a . An Improved Stability Criterion for Systems with Distributed Delays . International Journal of Robust & Nonlinear Control , 13 : 819 – 831 .
   Web of Science ®Google Scholar
• Gu , K . 2003b . Refined Discretised Lyapunov Functional Method for Systems with Multiple Delays . International Journal of Robust & Nonlinear Control , 13 : 1017 – 1033 .
   Web of Science ®Google Scholar
• Gu , K , Han , Q-L , Luo , ACJ and Niculescu , S-I . 2001 . Discretized Lyapunov Functional for Systems with Distributed Delay and Piecewise Constant Coefficients . International Journal of Control , 74 : 737 – 744 .
   Web of Science ®Google Scholar
• Gu , K , Kharitonov , VL and Chen , J . 2003 . Stability of Time-Delay Systems , Boston : Birkhäuser .
   Google Scholar
• Gu , K and Niculescu , S-I . 2000 . Additional Dynamics Introduced in Model System Transformation . IEEE Transactions on Automatic Control , 45 : 572 – 575 .
   Web of Science ®Google Scholar
• Gu , K and Niculescu , S-I . 2001 . Further Remarks on Additional Dynamics Introduced in Various Model Transformations of Linear Delay Systems . IEEE Transactions on Automatic Control , 46 : 497 – 500 .
   Web of Science ®Google Scholar
• Gu , K and Niculescu , S-I . 2003 . Survey on Recent Results in the Stability and Control of Time-delay Systems . Journal of Dynamic Systems, Measurement, and Control , 125 : 158 – 165 .
   Web of Science ®Google Scholar
• Guan , Z-H , Chen , W-H and Xu , J . 2005 . Delay-dependent Stability and Stabilisability of Uncertain Jump Bilinear Stochastic Systems with Mode-dependent Time-delays . International Journal of Systems Science , 36 : 275 – 285 .
   Web of Science ®Google Scholar
• Halanay , A . 1966 . Differential Equations: Stability, Oscillations, Time Lags , New York : Academic Press .
   Google Scholar
• Hale , JK . 1977 . Theory of Functional Differential Equations , New York : Springer-Verlag .
   Google Scholar
• Hale , JK and Verduyn Lunel , SM . 1993 . Introduction to Functional Differential Equations , New York : Springer-Verlag .
   Google Scholar
• Han , Q-L . 2002 . New Results for Delay-dependent Stability of Linear Systems with Time-varying Delay . International Journal of Systems Science , 33 : 213 – 228 .
   Web of Science ®Google Scholar
• Han , Q-L . 2003a . Stability Criteria for a Class of Linear Neutral Systems with Time-varying Discrete and Distributed Delays . IMA Journal of Mathematical Control Information , 20 : 371 – 386 .
   Google Scholar
• Han , Q-L . June 2003b . “ A Descriptor System Approach to Robust Stability of Uncertain Neutral Systems with Discrete and Distributed Delays ” . In in Proceedings of American Control Conference June , 5098 – 5103 . Denver, Colorado
   Google Scholar
• Han , Q-L . 2004 . A Descriptor System Approach to Robust Stability of Uncertain Neutral Systems with Discrete and Distributed Delays . Automatica , 40 : 1791 – 1796 .
   Web of Science ®Google Scholar
• Han , Q-L . 2005a . Absolute Stability of Time-delay Systems with Sector-bounded Nonlinearity . Automatica , 41 : 2171 – 2176 .
   Web of Science ®Google Scholar
• Han , Q-L . 2005b . A New Delay-dependent Stability Criterion for Linear Neutral Systems with Norm-bounded Uncertainties in All System Matrices . International Journal of Systems Science , 36 : 469 – 475 .
   Web of Science ®Google Scholar
• Han , Q-L . 2005c . On Stability of Linear Neutral Systems with Mixed Time Delays: A Discretised Lyapunov Functional Approach . Automatica , 41 : 1209 – 1218 .
   Web of Science ®Google Scholar
• Han , Q-L . 2007 . New Delay-dependent Synchronization Criteria for Lur'e Systems using Time Delay Feedback Control . Physics Letters A , 360 : 563 – 569 .
   Web of Science ®Google Scholar
• Han , Q-L and Gu , K . 2001 . On Robust Stability of Time-delay Systems with Norm-bounded Uncertainty . IEEE Transactions on Automatic Control , 46 : 1426 – 1431 .
   Web of Science ®Google Scholar
• Han , Q-L , Gu , K and Yu , X . 2003 . An Improved Estimate of the Robust Stability Bound of Time-delay Systems with Norm-bounded Uncertainty . IEEE Transactions on Automatic Control , 48 : 1629 – 1634 .
   Web of Science ®Google Scholar
• Han , Q-L , Yu , X and Gu , K . 2004 . On Computing the Maximum Time-delay Bound for Stability of Linear Neutral Systems . IEEE Transactions on Automatic Control , 49 : 2281 – 2285 .
   Web of Science ®Google Scholar
• He , Y , Wang , Q-G , Lin , C and Wu , M . 2005 . Augmented Lyapunov Functional and Delay-dependent Stability Criteria for Neutral Systems . International Journal of Robust & Nonlinear Control , 15 : 923 – 933 .
   Web of Science ®Google Scholar
• He , Y , Wang , Q-G , Lin , C and Wu , M . 2007 . Delay-range-dependent Stability for Systems with Time-varying Delay . Automatica , 43 : 371 – 376 .
   Web of Science ®Google Scholar
• He , Y , Wu , M , She , J-H and Liu , G-P . 2004a . Delay-dependent Robust Stability Criteria for Uncertain Neutral Systems with Mixed Delays . Systems & Control Letters , 51 : 57 – 65 .
   Web of Science ®Google Scholar
• He , Y , Wu , M , She , J-H and Liu , G-P . 2004b . Parameter-dependent Lyapunov Functional for Stability of Time-delay Systems with Polytopic-type Uncertainties . IEEE Transactions on Automatic Control , 49 : 828 – 832 .
   Web of Science ®Google Scholar
• Hmamed , A . 2000 . Constrained Regulation of Linear Discrete-time Systems with Time Delay: Delay-dependent and Delay-independent Conditions . International Journal of Systems Science , 31 : 529 – 536 .
   Web of Science ®Google Scholar
• Huang , H , Li , H-X and Zhong , J . 2006 . Master-slave Synchronization of General Lur'e Systems with Time-varying Delay and Parameter Uncertainty . International Journal of Bifurcation and Chaos in Applied Science and Engineering , 16 : 281 – 294 .
   Web of Science ®Google Scholar
• Hui , G-D and Hu , G-D . 1997 . Simple Criteria for Stability of Neutral Systems with Multiple Delays . International Journal of Systems Science , 28 : 1325 – 1328 .
   Web of Science ®Google Scholar
• Ismail , A and Mahmoud , MS . 2004 . A Descriptor Approach to Simulataneous H 2/H ∞ Control of Jumping Time-delay Systems . IMA Journal of Mathematical Control and Information , 21 : 95 – 114 .
   Google Scholar
• Ivanescu , D , Niculescu , S-I , Dugard , L , Dion , J-M and Verriest , EI . 2003 . On Delay-dependent Stability for Linear Neutral Systems . Automatica , 39 : 255 – 261 .
   Web of Science ®Google Scholar
• Jiang , X and Han , Q-L . 2005 . On H ∞ Control for Linear Systems with Interval Time-varying Delay . Automatica , 41 : 2099 – 2106 .
   Web of Science ®Google Scholar
• Jing , X-J , Tan , D-L and Wang , Y-C . 2004 . An LMI Approach to Stability of Systems with Severe Time-delay . IEEE Transactions on Automatic Control , 49 : 1192 – 1195 .
   Web of Science ®Google Scholar
• Khargonekar , PP , Petersen , IR and Zhou , K . 1990 . Robust Stabilisation of Uncertain Linear Systems: Quadratic Stabilisability and H ∞ Control Theory . IEEE Transactions on Automatic Control , 35 : 356 – 361 .
   Web of Science ®Google Scholar
• Kharitonov , VL and Melchor-Aguilar , D . 2000 . On Delay-dependent Stability Conditions . Systems & Control Letters , 40 : 71 – 76 .
   Web of Science ®Google Scholar
• Kharitonov , VL and Melchor-Aguilar , D . 2002 . On Delay-dependent Stability Conditions for Time-varying Systems . Systems & Control Letters , 46 : 173 – 180 .
   Web of Science ®Google Scholar
• Kharitonov , V and Melchor-Aguilar , D . 2003a . Additional Dynamics for General Class of Time-delay Systems . IEEE Transactions on Automatic Control , 48 : 1060 – 1064 .
   Web of Science ®Google Scholar
• Kharitonov , VL and Melchor-Aguilar , D . 2003b . Lyapunov-Krasovskii Functionals for Additional Dynamics . International Journal of Robust & Nonlinear Control , 13 : 793 – 804 .
   Web of Science ®Google Scholar
• Kim , J-H . 2001 . Delay and Its Time-derivative Dependent Robust Stability of Time-delayed Linear Systems with Uncertainty . IEEE Transactions on Automatic Control , 46 : 789 – 792 .
   Web of Science ®Google Scholar
• Kolmanovskii , VB and Myshkis , AD . 1992 . Applied Theory of Functional Differential Equations , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Kolmanovskii , VB and Myshkis , AD . 1999 . Introduction to the Theory and Applications of Functional Differential Equations , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Kolmanovskii , VB , Niculescu , S-I and Richard , J-P . 1999 . On the Liapunov-Krasovskii Functionals for Stability Analysis of Linear Delay Systems . International Journal of Control , 72 : 374 – 384 .
   Web of Science ®Google Scholar
• Kolmanovskii , VB and Richard , J-P . 1999 . Stability of Some Linear Systems with Delays . IEEE Transactions on Automatic Control , 44 : 984 – 989 .
   Web of Science ®Google Scholar
• Kwon , OM and Park , JH . 2006 . Guaranteed Cost Control for Uncertain Large-scale Systems with Time-delays via Delayed Feedback . Chaos, Solitons & Fractals , 27 : 800 – 812 .
   Web of Science ®Google Scholar
• Lam , H-K and Leung , FHF . 2006 . Design and Stabilisation of Sampled-data Neural-network-based Control Systems . IEEE Transactions on Systems, Man, Cybernetics. Part B , 36 : 995 – 1005 .
   PubMed Web of Science ®Google Scholar
• Lam , J , Gao , H and Wang , C . 2005 . H ∞ Model Reduction of Linear Systems with Distributed Delay . IEE Proceedings of Control Theory and Applications , 152 : 662 – 674 .
   Google Scholar
• Lam , J , Gao , H and Wang , C . 2007 . Stability Analysis for Continuous Systems with Two Additive Time-varying Delay Components . Systems & Control Letters , 56 : 16 – 24 .
   Web of Science ®Google Scholar
• Lee , YS , Moon , YS , Kwon , WH and Park , PG . 2004 . Delay-dependent Robust H ∞ Control for Uncertain Systems with a State-delay . Automatica , 40 : 65 – 72 .
   Web of Science ®Google Scholar
• Li , C , Wang , H and Liao , X . 2004 . Delay-dependent Robust Stability of Uncertain Fuzzy Systems with Time-varying Delays . IEE Proceedings of Control Theory and Applications , 151 : 417 – 421 .
   Google Scholar
• Li , X and de Souza , CE . 1997a . Criteria for Robust Stability and Stabilisation of Uncertain Linear Systems with State-delay . Automatica , 33 : 1657 – 1662 .
   Web of Science ®Google Scholar
• Li , X and de Souza , CE . 1997b . Delay-dependent Robust Stability and Stabilisation of Uncertain Linear Delay Systems: A Linear Matrix Inequality Approach . IEEE Transactions on Automatic Control , 42 : 1144 – 1148 .
   Web of Science ®Google Scholar
• Lien , C-H . 2001 . New Stability Criterion for a Class of Uncertain Nonlinear Neutral Time-delay Systems . International Journal of Systems Science , 32 : 215 – 219 .
   Web of Science ®Google Scholar
• Lien , CH . 2005 . Delay-dependent Stability Criteria for Uncertain Neutral Systems with Multiple Time-varying Delays via LMI Approach . IEE Proceedings of Control Theory and Applications , 152 : 707 – 714 .
   Google Scholar
• Lien , C-H . 2006 . Further Results on Delay-dependent Robust Stability of Uncertain Fuzzy Systems with Time-varying Delay . Chaos, Solitons & Fractals , 28 : 422 – 427 .
   Web of Science ®Google Scholar
• Lien , C-H and Chen , J-D . 2003 . Discrete-delay-independent and Discrete-delay-dependent Criteria for a Class of Neutral Systems . ASME Journal of Dynamic Systems, Measurement and Control , 125 : 33 – 41 .
   Web of Science ®Google Scholar
• Lien , C-H , Yu , K-W and Hsieh , J-G . 2000 . Stability Conditions for a Class of Neutral Systems with Multiple Time Delays . Journal of Mathematical Analysis Applications , 245 : 20 – 27 .
   Web of Science ®Google Scholar
• Lin , C , Wang , Q-G and Lee , TH . 2006a . A Less Conservative Robust Stability Test for Linear Uncertain Time-delay Systems . IEEE Transactions on Automatic Control , 51 : 87 – 91 .
   Web of Science ®Google Scholar
• Lin , C , Wang , Q-G and Lee , TH . 2006b . Less Conservative Stability Conditions for Fuzzy Large-scale Systems with Time Delays . Chaos, Solitons & Fractals , 29 : 1147 – 1154 .
   Web of Science ®Google Scholar
• Lin , C , Wang , Q-G and Lee , TH . 2006c . Delay-dependent LMI Conditions for Stability and Stabilisation of T-S Fuzzy Systems with Bounded Time-delay . Fuzzy Sets and Systems , 157 : 1229 – 1247 .
   Web of Science ®Google Scholar
• Liu , P-L . 2001 . Robust Stability of Multiple-time-delay Uncertain Systems with Series Nonlinearity . International Journal of Systems Science , 32 : 185 – 193 .
   Web of Science ®Google Scholar
• Liu , P-L and Su , T-J . 1998 . Robust Stability of Interval Time-delay Systems with Delay-dependence . Systems & Control Letters , 33 : 231 – 239 .
   Web of Science ®Google Scholar
• Liu , P-L and Su , T-J . 1999 . Stability for Single and Large-scale Uncertain Systems with Time-varying Delays . IEE Proceedings of Control Theory and Applications , 146 : 591 – 597 .
   Google Scholar
• Liu , X and Zhang , H . 2005 . New Stability Criterion of Uncertain Systems with Time-varying Delay . Chaos, Solitons & Fractals , 26 : 1343 – 1348 .
   Web of Science ®Google Scholar
• Liu , X , Zhang , H and Zhang , F . 2005 . Delay-dependent Stability of Uncertain Fuzzy Large-scale Systems with Time Delays . Chaos, Solitons & Fractals , 26 : 147 – 158 .
   Web of Science ®Google Scholar
• Liu , XG , Martin , RR , Wu , M and Tang , ML . 2006 . Delay-dependent Robust Stabilisation of Discrete-time Systems with Time-varying Delay . IEE Proceedings of Control Theory and Applications , 153 : 689 – 702 .
   Google Scholar
• Lou , X and Cui , B . 2007 . Delay-dependent Stochastic Stability of Delayed Hopfield Neural Networks with Markovian Jump Parameters . Journal of Mathematical Analysis and Applications , 328 : 316 – 326 .
   Web of Science ®Google Scholar
• Lu , G , Ho , DWC and Yeung , LF . 2003 . Strict Positive Realness for Linear Time-delay Systems . International Journal of Systems Science , 34 : 1 – 9 .
   Web of Science ®Google Scholar
• Luo , RC and Chung , L-Y . 2002 . Stabilization for Linear Uncertain System with Time Latency . IEEE Transactions on Industrial Electronics , 49 : 905 – 910 .
   Web of Science ®Google Scholar
• Mahmoud , MS , Shi , Y and Nounou , HN . 2007 . Resilient Observer-based Control of Uncertain Time-delay Systems . International Journal of Innovative Computing, Information and Control , 3 : 407 – 418 .
   Web of Science ®Google Scholar
• Moon , YS , Park , P , Kwon , WH and Lee , YS . 2001 . Delay-dependent Robust Stabilisation of Uncertain State-delayed Systems . International Journal of Control , 74 : 1447 – 1455 .
   Web of Science ®Google Scholar
• Niculescu , S-I . 2001a . Delay Effects on Stability: A Robust Control Approach , Berlin : Springer .
   Google Scholar
• Niculescu , S-I . 2001b . On Delay-dependent Stability Under Model Transformations of Some Neutral Linear Systems . International Journal of Control , 74 : 609 – 617 .
   Web of Science ®Google Scholar
• Niculescu , S-I , Dion , J-M and Dugard , L . 1996 . Robust Stabilisation for Uncertain Time-delay Systems Containing Saturating Actuators . IEEE Transactions on Automatic Control , 41 : 742 – 747 .
   Web of Science ®Google Scholar
• Niu , Y and Ho , DW . 2006 . Robust Observer Design for Ito Stochastic Time-delay Systems via Sliding Mode Control . Systems & Control Letters , 55 : 781 – 793 .
   Web of Science ®Google Scholar
• Niu , Y , Ho , DWC and Lam , J . 2005 . Robust Integral Sliding Mode Control for Uncertain Stochastic Systems with Time-varying Delay . Automatica , 41 : 873 – 880 .
   Web of Science ®Google Scholar
• Palhares , RM , Campos , CD , Ekel , PY , Leles , MCR and D'Angelo , MFSV . 2005a . Delay-dependent Robust H ∞ Control of Uncertain Linear Systems with Time-varying Delays . Computers and Mathematics with Applications , 50 : 13 – 32 .
   Web of Science ®Google Scholar
• Palhares , RM , Campos , CD , Ekel , PY , Leles , MCR and D'Angelo , MFSV . 2005b . Delay-dependent Robust H ∞ Control of Uncertain Linear Systems with Lumped Delays . IEE Proceedings of Control Theory and Applications , 153 : 27 – 33 .
   Google Scholar
• Park , J-H . 2001 . A New Delay-dependent Criterion for Neutral Systems with Multiple Delays . Journal of Computational and Applied Mathematics , 136 : 177 – 184 .
   Web of Science ®Google Scholar
• Park , JH . 2005 . Design of Dynamic Controller for Neutral Differential Systems with Delay in Control Input . Chaos, Solitons & Fractals , 23 : 503 – 509 .
   Web of Science ®Google Scholar
• Park , JH and Kwon , O . 2005 . On New Stability Criterion for Delay-differential Systems of Neutral Type . Applied Mathematics and Computation , 162 : 627 – 637 .
   Web of Science ®Google Scholar
• Park , P . 1999 . A Delay-dependent Stability Criterion for Systems with Uncertain Time-invariant Delays . IEEE Transactions on Automatic Control , 44 : 876 – 877 .
   Web of Science ®Google Scholar
• Parlakci , NNA . 2006 . Robust Stability of Uncertain Time-varying State-delayed Systems . IEE Proceedings of Control Theory and Applications , 152 : 469 – 477 .
   Google Scholar
• Peaucelle , D , Arzelier , D , Henrion , D and Gouaisbaut , F . 2007 . Quadratic Separation for Feedback Connection of an Uncertain Matrix and an Implicit Linear Transformation . Automatica , 43 : 795 – 804 .
   Web of Science ®Google Scholar
• Richard , J-P . 2003 . Time-delay Systems: an Overview of Some Recent Advances and Open Problems . Automatica , 39 : 1667 – 1694 .
   Web of Science ®Google Scholar
• Shi , P , Agarwal , RK , Boukas , EK and Shue , S-P . 2000 . Robust H ∞ State Feedback Control of Discrete Time-delay Linear Systems with Norm-bounded Uncertainty . International Journal of Systems Science , 31 : 409 – 415 .
   Web of Science ®Google Scholar
• Shi , P , Zhang , J , Qiu , L and Xing , L . 2007 . New Global Asymptotic Stability Criterion for Neural Networks with Discrete and Distributed Delays . Proceedings of the Institution of Mechanical Engineering Part I–Journal of Systems and Control Engineering , 221 : 129 – 135 .
   Web of Science ®Google Scholar
• Shu , Z , Lam , J and Xu , S . 2006 . Robust Stabilisation of Markovian Delay Systems with Delay-dependent Exponential Estimates . Automatica , 42 : 2001 – 2008 .
   Web of Science ®Google Scholar
• Su , H and Chu , J . 1999 . Robust H ∞ Control for Linear Time-varying Uncertain Time-delay Systems via Dynamic Output Feedback . International Journal of Systems Science , 30 : 1093 – 1107 .
   Web of Science ®Google Scholar
• Su , T-J and Huang , C . 1992 . Robust Stability of Delay Dependence for Linear Uncertain Systems . IEEE Transactions on Automatic Control , 37 : 1656 – 1659 .
   Web of Science ®Google Scholar
• Sun , X-M , Zhao , J and Wang , W . 2007 . Two Design Schemes for Robust Adaptive Control of a Class of Linear Uncertain Neutral Delay Systems . International Journal of Innovative Computing Information and Control , 3 : 385 – 396 .
   Web of Science ®Google Scholar
• Sun , YG , Wang , L and Xie , G . 2006 . Delay-dependent Robust Stability and Stabilisation for Discrete-time Switched Systems with Mode-dependent Time-varying Delays . Applied Mathematics and Computation , 180 : 428 – 435 .
   Web of Science ®Google Scholar
• Suplin , V , Fridman , E and Shaked , U . 2004 . “ A Projection Approach to H ∞ Control of Time-delay Systems ” . In in Proceedings of 43rd IEEE Conference Decision and Control 4548 – 4553 . Atlantis, Bahamas, , USA December
   Google Scholar
• Suplin , V , Fridman , E and Shaked , U . 2006 . H ∞ Control of Linear Uncertain Time-delay Systems–A Projection Approach . IEEE Transactions on Automatic Control , 51 : 680 – 685 .
   Web of Science ®Google Scholar
• Tarbouriech , S , Peres , PLD , Garcia , G and Queinnec , I . 2002 . Delay-dependent Stabilisation and Disturbance Tolerance for Time-delay Systems Subject to Actuator Saturation . IEE Proceedings of Control Theory and Applications , 149 : 387 – 393 .
   Google Scholar
• Verriest , EI , Fan , MKH and Kullstam , J . 1993 . “ Frequency Domain Robust Stability Criteria for Linear Delay Systems ” . In in Proceedings of 32nd IEEE Conference Decision and Control 3473 – 3478 . San Antonio, Texas December
   Google Scholar
• Wang , Z and Unbehauen , H . 2000 . Nonlinear Observers for a Class of Continuous-time Uncertain State Delayed Systems . International Journal of Systems Science , 31 : 555 – 562 .
   Web of Science ®Google Scholar
• Wu , H-N . 2006 . Delay-dependent Stability Analysis and Stabilisation for Discrete-time Fuzzy Systems with State Delay: A Fuzzy Lyapunov-Krasovskii Functional Approach . IEEE Transactions on Systems, Man, Cybernet. Part B , 36 : 954 – 962 .
   PubMed Web of Science ®Google Scholar
• Wu , J , Chen , T and Wang , L . 2006 . Delay-dependent Robust Stability and H ∞ Control for Jump Linear Systems with Delays . Systems & Control Letters , 55 : 939 – 948 .
   Web of Science ®Google Scholar
• Wu , L , Shi , P , Wang , C and Gao , H . 2006 . Delay-dependent Robust H ∞ and L 2 − L ∞ Filtering for LPV Systems with Both Discrete and Distributed Delays . IEE Proceedings of Control Theory and Applications , 153 : 483 – 492 .
   Google Scholar
• Wu , M , He , Y and She , J-H . 2004 . New Delay-dependent Stability Criteria and Stabilising Method for Neutral Systems . IEEE Transactions on Automatic Control , 49 : 2266 – 2271 .
   Web of Science ®Google Scholar
• Wu , M , He , Y and She , J-H . 2006 . Delay-dependent Stabilisation for Systems with Multiple Unknown Time-varying Delays . International Journal of Control, Automation, and Systems , 6 : 682 – 688 .
   Google Scholar
• Wu , M , He , Y , She , J-H and Liu , G-P . 2004 . Delay-dependent Criteria for Robust Stability of Time-varying Delay Systems . Automatica , 40 : 1435 – 1439 .
   Web of Science ®Google Scholar
• Xie , N and Tang , G-Y . 2006 . Delay-dependent Nonfragile Guaranteed Cost Control for Nonlinear Time-delay Systems . Nonlinear Analysis , 64 : 2084 – 2097 .
   Web of Science ®Google Scholar
• Xu , S and Lam , J . 2005 . Improved Delay-dependent Stability Criteria for Time-delay Systems . IEEE Transactions on Automatic Control , 50 : 384 – 387 .
   Web of Science ®Google Scholar
• Xu , S and Lam , J . 2007 . On Equivalence and Efficiency of Certain Stability Criteria for Time-delay Systems . IEEE Transactions on Automatic Control , 52 : 95 – 101 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J , Chen , T and Zou , Y . 2005 . A Delay-dependent Approach to Robust H ∞ Filtering for Uncertain Distributed Delay Systems . IEEE Transactions on Signal Processing , 53 : 3764 – 3772 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J , Ho , DWC and Zou , Y . 2005 . Delay-dependent Exponential Stability for a Class of Neural Networks with Time Delays . Journal of Computational and Applied Mathematics , 183 : 16 – 28 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J , Mao , X and Zou , Y . 2005 . A New LMI Condition for Delay-dependent Robust Stability of Stochastic Time-delay Systems . Asian Journal of Control , 7 : 419 – 423 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J and Yang , C . 2002 . Robust Stability Analysis and Stabilisation for Uncertain Linear Neutral Delay Systems . International Journal of Systems Science , 33 : 1195 – 1206 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J and Zou , Y . 2005a . Further Results on Delay-dependent Robust Stability Conditions of Uncertain Neutral Systems . International Journal of Robust & Nonlinear Control , 15 : 233 – 246 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J and Zou , Y . 2005b . Improved Conditions on Delay-dependent Robust Stability and Stabilisation of Uncertain Discrete Time-delay Systems . Asian Journal of Control , 7 : 344 – 348 .
   Web of Science ®Google Scholar
• Xu , S , Lam , J and Zou , Y . 2005c . Simplified Descriptor System Approach to Delay-dependent Stability and Performance Analyses for Time-delay Systems . IEE Proceedings of Control Theory and Applications , 152 : 147 – 151 .
   Google Scholar
• Xu , S , Lam , J and Zou , Y . 2006a . Delay-dependent Guaranteed Cost Control for Uncertain Systems with Both State and Input Delays . IEE Proceedings of Control Theory and Applications , 153 : 307 – 313 .
   Google Scholar
• Xu , S , Lam , J and Zou , Y . 2006b . New Results on Delay-dependent Robust H ∞ Control for Systems with Time-varying Delays . Automatica , 42 : 343 – 348 .
   Web of Science ®Google Scholar
• Xu , S , Van Dooren , P , Stefan , R and Lam , J . 2002 . Robust Stability and Stabilisation for Singular Systems with State Delay and Parameter Uncertainty . IEEE Transactions on Automatic Control , 47 : 1122 – 1128 .
   Web of Science ®Google Scholar
• Yoneyama , J . 2007 . Robust Stability and Stabilisation for Uncertain Takagi-Sugeno Fuzzy Time-delay Systems . Fuzzy Sets and Systems , 158 : 115 – 134 .
   Web of Science ®Google Scholar
• Yu , L , Han , Q-L , Yu , S and Gao , J . 2003 . “ Delay-dependent Conditions for Robust Absolute Stability of Uncertain Time-delay Systems ” . In Proceedings of 42nd IEEE Conference Decision and Control 6033 – 6037 . Maui, Hawaii, , USA December
   Google Scholar
• Yue , D and Han , Q-L . 2004 . “ A Delay-dependent Stability Criterion of Neutral Systems and Its Application to a Partial Element Equivalent Circuit Model ” . In in Proceedings of American Control Conference 5438 – 5442 . Boston, Massachusetts
   Google Scholar
• Yue , D and Han , Q-L . 2005a . Delay-dependent Exponential Stability of Stochastic Systems with Time-varying Delay, Nonlinearity, and Markovian Switching . IEEE Transactions on Automatic Control , 50 : 217 – 222 .
   Web of Science ®Google Scholar
• Yue , D and Han , Q-L . 2005b . Delay-dependent Robust H ∞ Controller Design for Uncertain Descriptor Systems with Time-varying Discrete and Distributed Delays . IEE Proceedings of Control Theory and Applications , 152 : 628 – 638 .
   Google Scholar
• Zhang , X-M , Wu , M , She , J-H and He , Y . 2005 . Delay-dependent Stabilisation of Linear Systems with Time-varying State and Input Delays . Automatica , 41 : 1405 – 1412 .
   Web of Science ®Google Scholar
• Zhao , Y , Gao , H , Lam , J and Du , B . 2008 . Stability and Stabilisation of Delayed T-S Fuzzy Systems: A Delay Partitioning Approach . IEEE Transactions on Fuzzy Systems , (to appear)
   Web of Science ®Google Scholar
• Zheng , F and Frank , PM . 2002 . Robust Control of Uncertain Distributed Delay Systems with Application to the Stabilisation of Combustion in Rocket Motor Chambers . Automatica , 38 : 487 – 497 .
   Web of Science ®Google Scholar
• Zhou , S and Li , T . 2005 . Robust Stabilisation for Delayed Discrete-time Fuzzy Systems via Basis-dependent Lyapunov-Krasovskii Function . Fuzzy Sets and Systems , 151 : 139 – 153 .
   Web of Science ®Google Scholar