Generalised finite-frequency KYP lemma in delta domain and applications to fault detection

References

• Aldeen , M and Sharma , R . 2007 . Robust Detection of Faults in Frequency Control Loops . IEEE Transactions on Power Systems , 22 : 413 – 422 .
   Web of Science ®Google Scholar
• Amato , F , Cosentino , C , Mattei , M and Paviglianiti , G . 2006 . A Direct/Functional Redundancy Scheme for Fault Detection and Isolation on an Aircraft . Aerospace Science and Technology , 10 : 338 – 345 .
   Web of Science ®Google Scholar
• Anderson , SR and Kadirkamanathan , V . 2007 . Modelling and Identification of Non-linear Deterministic Systems in the Delta-domain . Automatica , 43 : 1859 – 1868 .
   Web of Science ®Google Scholar
• Chen , J and Patton , RJ . 1999 . Robust Model-based Fault Diagnosis for Dynamic Systems , Boston, MA, , USA : Kluwer Academic Publisher .
   Google Scholar
• Collins Jr , EG and Song , T . 1999 . A Delta Operator Approach to Discrete-time H ∞ Control . International Journal of Control , 72 : 315 – 320 .
   Web of Science ®Google Scholar
• Fong , KF , Loh , AP and Tan , WW . 2007 . A Frequency Domain Approach for Fault Detection . International Journal of Control , 81 : 264 – 276 .
   Web of Science ®Google Scholar
• Gahinet , P and Apkarian , P . 1994 . A Linear Matrix Inequality Approach to H ∞ Control . International Journal of Robust Nonlinear Control , 4 : 421 – 448 .
   Web of Science ®Google Scholar
• Gahinet , P , Nemirovski , A , Laub , A and Chilali , M . 1995 . LMI Control Toolbox for Use with Matlab , Natick, MA : The Math Works Inc .
   Google Scholar
• Goodwin , GC , Lozano Leal , R , Mayne , DQ and Middleton , RH . 1986 . Rapprochement Between Continuous and Discrete Model Reference Adaptive Control . Automatica , 22 : 199 – 207 .
   Web of Science ®Google Scholar
• Green , M and Limebeer , DJN . 1995 . Linear Robust Control , Englewood Cliffs, NJ : Prentice-Hall, Inc .
   Google Scholar
• Hou , M and Patton , RJ . An LMI Approach to H −/H ∞ Fault Detection Observers . Proceedings of the UKACC international conference on control . 1996 . pp. 305 – 310 .
   Google Scholar
• Iwasaki , T and Hara , S . Generalization of Kalman--Yakubovic--Popov Lemma for Restricted Frequency Inequalities . American Control Conference . 2003 . Vol. 5 , pp. 3828 – 3833 .
   Google Scholar
• Iwasaki , T and Hara , S . 2005 . Generalized KYP Lemma: Unified Frequency Domain Inequalities with Design Applications . IEEE Transactions on Automatic Control , 50 : 41 – 59 .
   Web of Science ®Google Scholar
• Iwasaki , T , Hara , S and Fradkov , AL . Restricted Frequency Inequalities Equivalent to Restricted Dissipativity . The 43rd IEEE Conference on Decision and Control . 2004 . Vol. 14-17 , pp. 426 – 431 . Atlantis, Paradise, Island, Bahamas
   Google Scholar
• Iwasaki , T , Hara , S and Fradkov , AL . 2005 . Time Domain Interpretations of Frequency Domain Inequalities on (semi)finite Ranges . Systems and Control Letters , 54 : 681 – 691 .
   Web of Science ®Google Scholar
• Iwasaki , T , Hara , S and Yamauchi , H . 2003 . Dynamical System Design from a Control Perspective: Finite Frequency Positive Realness Approach . IEEE Transactions on Automatic Control , 48 : 1337 – 1354 .
   Web of Science ®Google Scholar
• Iwasaki , T , Meinsma , G and Fu , M . 2000 . Generalized S-procedure and Finite Frequency KYP Lemma . Malhernarical Problems in Engineering , 6 : 305 – 320 .
   Web of Science ®Google Scholar
• Jaimoukha , IM , Li , Z and Papakos , V . 2006 . A Matrix Factorisation Solution to the H −/H ∞ Fault Detection Problem . Automatica , 42 : 1907 – 1912 .
   Web of Science ®Google Scholar
• Kia , SH , Henao , H and Capolino , GA . 2007 . A High-resolution Frequency Estimation Method for Three-phase Induction Machine Fault Detection . IEEE Transactions on Industrial Electronics , 54 : 2305 – 2314 .
   Web of Science ®Google Scholar
• Li , X and de Sonza , CE . 1997 . 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
• Middleton , R and Goodwin , G . 1986 . Improved Finite Word Length Characteristics in Digital Control using Delta Operators . IEEE Transactions on Automatic Control , 31 : 1015 – 1021 .
   Web of Science ®Google Scholar
• Middleton , RH and Goodwin , GC . 1990 . Digital Control and Estimation , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Narendra , K and Tripathi , SS . 1973 . Identification and Optimisation of Aircraft Dynamics . American Institute of Aeronautics and Astronautics Journal of Aircraft , 10 : 193 – 199 .
   Google Scholar
• Peng, Z.K., Lang, Z.Q., and Billings, S.A. (2007), ‘The Nonlinear Output Frequency Response Function and its Application to Fault Detection’, in Fault Detection, Supervision and Safety of Technical Processes 2006, pp. 36--41
   Google Scholar
• Qiu, Z., and Gertler, J. (1993), ‘Robust FDI Systems and H ∞-optimisation’, in Proceedings of the 32nd Conference on Decision Control, San Antonio, Texas, pp. 1710--1715
   Google Scholar
• Qiu , J , Xia , Y , Yang , H and Zhang , J . 2008 . Robust Stabilisation for a Class of Discrete-time Systems with Time-varying Delays via Delta Operators . IET Control Theory and Applications , 2 : 87 – 93 .
   Web of Science ®Google Scholar
• Suchomski , P . 2002 . A J-lossless Coprime Factorisation Approach to H ∞ Control in Delta Domain . Automatica , 38 : 1807 – 1814 .
   Web of Science ®Google Scholar
• Wang , H and Yang , G-H . 2008a . A Finite Frequency Domain Approach to Fault Detection Observer Design for Linear Continuous-time Systems . Asian Journal of Control , 10 : 1 – 10 .
   Web of Science ®Google Scholar
• Wang , H and Yang , G-H . 2008b . A Finite Frequency Domain Approach to Fault Detection for Linear Discrete-time Systems . International Journal of Control , 81 : 1162 – 1171 .
   Web of Science ®Google Scholar
• Wang , J , Yang , G-H and Liu , J . 2007 . An LMI Approach to H − Index and Mixed H −/H ∞ Fault Detection Observer Design . Automatica , 43 : 1656 – 1665 .
   Web of Science ®Google Scholar
• Yang , RH and Lim , YC . 1996 . A Dynamic Frequency Grid Allocation Scheme for the Efficient Design of Equiripple FIR Filters . IEEE Transactions on Signal Processing , 44 : 2335 – 2339 .
   Web of Science ®Google Scholar
• Yang , H , Xia , Y , Fu , M and Shi , P . 2010 . Robust Adaptive Sliding Mode Control for Uncertain Delta Operator Systems . International Journal of Adaptive Control and Signal Processing , 24 : 623 – 632 .
   Web of Science ®Google Scholar
• Yang , H , Xia , Y , Qiu , J and Zhang , J . 2010 . Filtering for a Class of Discrete-time Systems with Time-delays via Delta Operator Approach . International Journal of Systems Science , 41 : 423 – 433 .
   Web of Science ®Google Scholar
• Ye , H , Ding , SX and Wang , G . 2002 . Integrated Design of Fault Detection Systems in Time-frequency Domain . IEEE Transactions on Automatic Control , 47 : 384 – 390 .
   Web of Science ®Google Scholar
• Zhang , P , Ding , SX , Wang , GZ and Zhou , DH . 2003 . A Frequency Domain Approach to Fault Detection in Sampled-data Systems . Automatica , 39 : 1303 – 1307 .
   Web of Science ®Google Scholar