Stability analysis and stabilisation for a class of 2-D nonlinear discrete systems

References

• Benzaouia , A , Akhrif , O and Saydy , L . 2010 . Stabilisation and Control Synthesis of Switching Systems Subject to Actuator Saturation . International Journal of Systems Science , 41 : 397 – 409 .
   Web of Science ®Google Scholar
• Benzaouia , A , Benmessaouda , O and Shi , Y . 2009 . Output Feedback Stabilization of Uncertain Saturated Discrete-time Switching Systems . International Journal of Innovative Computing, Information and Control , 5 : 1735 – 1746 .
   Google Scholar
• Boukas , EK . 2008 . Free-weighting Matrices Delay-dependent Stabilization for Systems with Time-varying Delays . IcIC Express Letters , 2 : 167 – 173 .
   Google Scholar
• Boukas , EK and M'Sirdi , NK . 2008 . Stabilization of Linear Systems via Delayed State Feedback Controller . ICIC Express Letters , 2 : 1 – 6 .
   Google Scholar
• Cao , YY , Lin , Z and Chen , BM . 2003 . An Output Feedback H ∞ Controller Design for Linear Systems Subject to Sensor Nonlinearities . IEEE Transactions on, Circuits and Systems I: Fundamental Theory and Applications , 50 : 914 – 921 .
   Google Scholar
• Du , C and Xie , L . 1999 . Stability Analysis and Stabilization of Uncertain Two-dimensional Discrete Systems: An LMI Approach . IEEE Transactions on, Circuits and Systems I: Fundamental Theory and Applications , 46 : 1371 – 1374 .
   Google Scholar
• Du , C and Xie , L . 2002 . H _∞ Control and Filtering of Two-dimensional Systems , Berlin : Springer-Verlag .
   Google Scholar
• Du , C , Xie , L and Zhang , C . 2000 . Solutions for H ∞ Filtering of Two-dimensional Systems . Multidimensional Systems and Signal Processing , 11 : 301 – 320 .
   Google Scholar
• Du , C , Xie , L and Zhang , C . 2001 . H ∞ Control and Robust Stabilization of Two-dimensional Systems in Roesser Models . Automatica , 37 : 205 – 211 .
   Web of Science ®Google Scholar
• Gahinet , P and Apkarian , P . 1994 . A Linear Matrix Inequality Approach to H ∞ Control . International Journal of Robust and Nonlinear Control , 4 : 421 – 448 .
   Web of Science ®Google Scholar
• Guan , X , Long , C and Duan , G . 2001 . Robust Optimal Guaranteed Cost Control for 2D Discrete Systems . IEE Proceedings on Control Theory and Applications , 148 : 355 – 361 .
   Google Scholar
• Iwasaki , T and Skelton , RE . 1994 . All Controllers for the General H ∞ Control Problem: LMI Existence Conditions and State Space Formulas . Automatica , 30 : 1307 – 1317 .
   Web of Science ®Google Scholar
• Kaczorek , T . 1984 . Two-Dimensional Linear Systems , New York : Springer-Verlag .
   Google Scholar
• Kaczorek , T and Klamka , J . 1988 . Minimum Energy Control for General Model of 2-D Linear Systems . International Journal of Control , 47 : 1555 – 1562 .
   Web of Science ®Google Scholar
• Kar , H and Singh , V . 2004 . Robust Stability of 2-D Discrete Systems Described by the Fornasini-Marchesini Second Model Employing Quantization/Overflow Nonlinearities . IEEE Transactions on Circuits and Systems II: Express Briefs , 51 : 598 – 602 .
   Web of Science ®Google Scholar
• Khalil , HK . 2002 . Nonlinear Systems , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Krishna , Rao , Kandanvli , V and Kar , H . 2009 . An LMI Condition for Robust Stability of Discrete-time State-delayed Systems using Quantization/Overflow Nonlinearities . Signal Processing , 89 : 2092 – 2102 .
   Google Scholar
• Lin , Z . 1998 . Feedback Stabilizability of MIMO n-D Linear Systems . Multidimensional Systems and Signal Processing , 9 : 149 – 172 .
   Web of Science ®Google Scholar
• Lin , W and Byrnes , CI . 1996 . H ∞-control of Discrete-time Nonlinear Systems . IEEE Transactions on Automatic Control , 41 : 494 – 510 .
   Web of Science ®Google Scholar
• Lin , Z , Galkowski , K and Wood , J . 2001 . Output Feedback Stabilizability and Stabilization of Linear n-D Systems . Multidimensional Signals, Circuits and Systems , 4 : 59 – 76 .
   Google Scholar
• Lin , Z , Ying , JQ and Xu , L . 2002 . An Algebraic Approach to Strong Stabilizability of Linear nD MIMO Systems . Automatic Control, IEEE Transactions on , 47 : 1510 – 1514 .
   Google Scholar
• Shi , T , Su , H and Chu , J . 2010 . On Stability and Stabilisation for Uncertain Stochastic Systems with Time-delay and Actuator Saturation . International Journal of Systems Science , 41 : 501 – 509 .
   Web of Science ®Google Scholar
• Singh , V . 2007 . Improved Criterion for Global Asymptotic Stability of 2-D Discrete Systems with State Saturation . IEEE Signal Processing Letters , 14 : 719 – 722 .
   Web of Science ®Google Scholar
• Singh , V . 2008 . Stability Analysis of 2-D Discrete Systems Described by the Fornasini-Marchesini Second Model with State Saturation . Circuits and Systems II: Express Briefs, IEEE Transactions on , 55 : 793 – 796 .
   Web of Science ®Google Scholar
• Wang , Y , Xie , L and de Souza , CE . 1992 . Robust Control of a Class of Uncertain Nonlinear Systems . Systems and Control Letters , 19 : 139 – 149 .
   Web of Science ®Google Scholar
• Xiao , Y and Unbehauen , R . 1998 . New Stability Test Algorithm for Two-dimensional Digital Filters . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 45 : 739 – 741 .
   Google Scholar
• Xu , S , Lam , J , Lin , Z , Galkowski , K , Paszke , W , Sulikowski , B , Rogers , E and Owens , DH . 2003b . Positive Real Control of Two-dimensional Systems: Roesser Models and Linear Repetitive Processes . International Journal of Control , 76 : 1047 – 1058 .
   Web of Science ®Google Scholar
• Xu , L , Saito , O and Abe , K . 1994 . Output Feedback Stabilizability and Stabilization Algorithms for 2D Systems . Multidimensional Systems and Signal Processing , 5 : 41 – 60 .
   Web of Science ®Google Scholar
• Xu , L , Wu , Q , Lin , Z and Anazawa , Y . 2004 . A μ Approach to Robust Stability Analysis of nD Discrete Systems . Multidimensional Systems and Signal Processing , 15 : 277 – 293 .
   Google Scholar
• Xu , L , Ying , J , Lin , Z and Saito , O . 2003a . Comments on “Stability Tests of N-dimensional Discrete Time Systems using Polynomial Arrays” . IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing , 50 : 666 – 669 .
   Google Scholar
• Xu , H , Zou , Y , Lu , J and Xu , S . 2005a . Robust H ∞ Control for a Class of Uncertain Nonlinear Two-dimensional Systems with State Delays . Journal of the Franklin Institute , 342 : 877 – 891 .
   Web of Science ®Google Scholar
• Xu , H , Zou , Y and Xu , S . 2005b . Robust H ∞ Control for a Class of Uncertain Nonlinear Two-dimensional Systems . International Journal of Innovational Computing and Information Control , 1 : 181 – 191 .
   Google Scholar
• Xu , H , Zou , Y and Xu , S . 2009 . Non-fragile Robust H ∞ Control for Uncertain 2-D Delayed Systems Described by the General Model . International Journal of Innovative Computing, Information and Control , 5 : 3179 – 3188 .
   Google Scholar
• Yang , R , Ntogramatzidis , L and Cantoni , M . 2009 . On the Realization of 2-D Linear Systems with Recursively Computable Latent Variable Models . IEEE Transactions on Circuits and Systems I: Regular Papers , 56 : 644 – 652 .
   Google Scholar
• Yang , R , Xie , L and Zhang , C . 2006 . H 2 and Mixed H 2/H ∞ Control of Two-dimensional Systems in Roesser Model . Automatica , 42 : 1507 – 1514 .
   Web of Science ®Google Scholar
• Yang , R , Xie , L and Zhang , C . 2008 . Generalized Two-dimensional Kalman-Yakubovich-Popov Lemma for Discrete Roesser Model . IEEE Transactions on Circuits and Systems I: Regular Papers , 55 : 3223 – 3233 .
   Web of Science ®Google Scholar
• Zuo , Z , Wang , J and Huang , L . 2005 . Output Feedback H ∞ Controller Design for Linear Discrete-time Systems with Sensor Nonlinearities . IEE Proceedings of Control Theory and Applications , 152 : 19 – 26 .
   Google Scholar