zbMATH — the first resource for mathematics

Fault detection filter design for switched systems with quantization effects. (English) Zbl 1347.93235
Summary: The problem of fault detection for switched systems with quantization effects is investigated in this paper. The dynamic quantizer introduced here is composed of a dynamic scaling and a static quantizer. Subsequently, a novel fault detection scheme, which fully considers the static quantizer range and quantizer error, is proposed. Furthermore, sufficient conditions for fault detection filter are given in the framework of linear matrix inequality, and the filter gains and the static quantizer range are obtained by a convex optimization problem. Finally, the presented technique is validated by two examples, and simulation results indicate that the proposed method can effectively detect the fault.

93E03 Stochastic systems in control theory (general)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
90C25 Convex programming
PDF BibTeX Cite
Full Text: DOI
[1] Daniel, Liberzon, Switching in systems and control, (2003), Birkhäuser Boston · Zbl 1036.93001
[2] Lin, Hai; Antsaklis Panos, J., Stability and stabilizability of switched linear systemsa survey of recent results, IEEE Trans. Autom. Control, 54, 2, 308-322, (2009) · Zbl 1367.93440
[3] Zhang, Lixian, H-infinity estimation for piecewise homogeneous Markov jump linear systems, Automatica, 45, 11, 2570-2576, (2009) · Zbl 1180.93100
[4] Du, Dongsheng; Bin, Jiang; Peng, Shi; Shaosheng, Zhou, \(\mathcal{H}_\infty\) filtering of discrete-time switched systems with state delays via switched Lyapunov function approach, IEEE Trans. Autom. Control, 52, 8, 1520-1525, (2007) · Zbl 1366.93652
[5] Hideaki, Ishii; Francis, Bruce A., Stabilizing a linear system by switching control with Dwell time, IEEE Trans. Autom. Control, 47, 12, 1962-1973, (2002) · Zbl 1364.93641
[6] Wang, Yue-E.; Sun, Xi-Ming; Zhao, Jun, Asynchronous H-infinity control of switched delay systems with average Dwell time, J. Frankl. Inst.—Eng. Appl. Math., 349, 10, 3159-3958, (2012) · Zbl 1255.93049
[7] Vu, Linh; Liberzon, Daniel, Common Lyapunov functions for families of commuting nonlinear systems, Syst. Control Lett., 54, 5, 405-416, (2005) · Zbl 1129.34321
[8] Zhang, Lixian; Wang, Changhong; Chen, Lingjie, Stability and stabilization of a class of multi-mode linear discrete-time systems with polytopic uncertainties, IEEE Trans. Ind. Electron., 56, 9, 3684-3692, (2009)
[9] Xiang, Weiming; Xiao, Jian; Naveed, Iqbal Muhammad, Robust fault detection for a class of uncertain switched nonlinear systems via the state updating approach, Nonlinear Anal.: Hybrid Syst., 12, 132-146, (2014) · Zbl 1291.93309
[10] Wang, Wen-June; Chen, Ying-Jen; Sun, Chung-Hsun, Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function, IEEE Trans. Syst. Man Cybern.—Part B: Cybern., 37, 3, 551-559, (2007)
[11] Su, Qingyu; Zhao, Jun, Stabilization of a class of switched systems with state constraints, Nonlinear Dyn., 70, 2, 1499-1510, (2012) · Zbl 1268.93123
[12] Lian, Jie; Liu, Jiao, New results on stability of switched positive systemsan average Dwell-time approach, IET Control Theory Appl., 7, 12, 1651-1658, (2013)
[13] Zhang, Lixian; Cui, Naigang; Liu, Ming; Zha, Ye, Asynchronous filtering of discrete-time switched linear systems with average Dwell time, IEEE Trans. Circuits Syst. I, 58, 5, 1109-1118, (2011)
[14] Hwang, Inseok; Kim, Sungwan; Kim, Youdan; Seah, Chze Eng, A survey of fault detection, isolation and reconfiguration methods, IEEE Trans. Control Syst. Technol., 18, 636-653, (2010)
[15] Zhong, M. Y.; Ding, S. X.; Lam, J.; Wang, H. B., An LMI approach to design robust fault detection filter for uncertain LTI systems, Automatica, 39, 3, 543-550, (2003) · Zbl 1036.93061
[16] Mao, Z.; Jiang, Bin; Shi, Peng, \(\mathcal{H}_\infty\) fault detection filter design for networked control systems modelled by discrete Markovian jump systems, IET Control Theory Appl., 1, 5, 1336-1343, (2007)
[17] Gao, H.; Chen, T.; Wang, L., Robust fault detection with missing measurements, Int. J. Control, 81, 5, 804-819, (2008) · Zbl 1152.93346
[18] Lee, Kee-Sang; Park, Tae-Geon, Robust fault detection observer design under fault sensitivity constraints, J. Frankl. Inst.—Eng. Appl. Math., 352, 5, 1791-1810, (2015) · Zbl 1395.93216
[19] Long, Yue; Yang, Guang-Hong, Fault detection and isolation for networked control systems with finite frequency specifications, Int. J. Robust Nonlinear Control, 24, 3, 495-514, (2014) · Zbl 1284.93027
[20] Wang, Dong; Wang, Wei; Shi, Peng, Robust fault detection for switched linear systems with state delays, IEEE Trans. Syst. Man Cybern.—Part B: Cybern., 39, 3, 800-805, (2009)
[21] Du, Dongsheng; Jiang, Bin; Shi, Peng, Fault detection for discrete-time switched systems with intermittent measurements, Int. J. Control, 85, 1, 78-87, (2012) · Zbl 1282.93255
[22] Li, Jiao; Zhao, Jun, Reliable H-infinity filtering for switched discrete-time systems with sensor failuresan estimated state-dependent switching method, J. Frankl. Inst.—Eng. Appl. Math., 350, 10, 3082-3099, (2013) · Zbl 1293.93740
[23] Li, Jian; Yang, Guang-Hong, Fault detection filter design for discrete-time switched linear systems with mode-dependent average Dwell-time, Int. J. Adapt. Control Signal Process., 28, 1, 77-95, (2014) · Zbl 1330.93227
[24] Zhong, GuangXin; Yang, GuangHong, Fault detection for uncertain switched systems with time-varying delays, J. Frankl. Inst.—Eng. Appl. Math., 352, 4, 1455-1475, (2015) · Zbl 1395.93163
[25] Liberzon, D., Hybrid feedback stabilisation of systems with quantised signals, Automatica, 39, 9, 1543-1554, (2003) · Zbl 1030.93042
[26] Wang, Zidong; Dong, Hongli; Shen, Bo; Gao, Huijun, Finite-horizon \(\mathcal{H}_\infty\) filtering with missing measurements and quantization effects, IEEE Trans. Autom. Control, 58, 7, 1707-1718, (2013) · Zbl 1369.93660
[27] Zhang, Lixian; Zhu, Yanzheng; Shi, Peng; Zhao, Yuxin, Resilient asynchronous H-infinity filtering for Markov jump neural networks with unideal measurements and multiplicative noises, IEEE Trans. Cybern., 45, 12, 2840-2852, (2015)
[28] Li, Mu; Sun, Jian; Dou, Lihua, Stability of an improved dynamic quantised system with time-varying delay and packet losses, IET Control Theory Appl., 9, 6, 988-995, (2015)
[29] Assaf, Gurt; Nair, Girish N., Internal stability of dynamic control for stochastic linear plants, Automatic, 45, 6, 1387-1396, (2009) · Zbl 1166.93380
[30] Guisheng Zhai, Xinkai Chen, Joe Imae, Tomoaki Kobayashi, Analysis and design of \(\mathcal{H}_\infty\) feedback control systems with two quantised signals, in: Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, 2006, pp. 346-350. · Zbl 1127.93355
[31] Che, W. W.; Wang, J. L.; Yang, G. H., Quantised \(\mathcal{H}_\infty\) filtering for networked systems with random sensor packet losses, IET Control Theory Appl., 4, 8, 1339-1352, (2010)
[32] Che, Weiwei; Yang, Guanghong, Quantised \(\mathcal{H}_\infty\) filter design for discrete-time systems, Int. J. Control, 82, 2, 195-206, (2009) · Zbl 1168.93406
[33] Frank, P. M.; Ding, X., Survey of robust residual generation and evaluation methods in observer-based fault detection systems, J. Process Control, 7, 6, 403-424, (1997)
[34] Xu, Honglei; Teo, Kok Lay, Exponential stability with L_{2}-gain condition of nonlinear impulsive switched systems, IEEE Trans. Autom. Control, 55, 10, 2429-2433, (2010) · Zbl 1368.93614
[35] Xu, H. L.; Liu, X. Z.; Teo, K. L., Robust \(\mathcal{H}_\infty\) stabilization with definite attenuance of uncertain impulsive switched systems, Anziam J., 46, 4, 471-484, (2005) · Zbl 1123.93073
[36] Li, Xiaojian; Yang, Guagnhong, Fault detection for linear stochastic systems with sensor stuck faults, Optim. Control Appl. Methods, 33, 1, 61-80, (2012) · Zbl 1258.93098
[37] Barkhordari, Yazdi M.; Jahed-Motlagh, M. R., Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization, Chem. Eng. J., 155, 3, 838-843, (2009)
[38] Magni, L.; Nicolao, G. D.; Magnani, L.; Scattolini, R., A stabilizing model-based predictive control algorithm for nonlinear systems, Automatica, 37, 9, 1351-1362, (2001) · Zbl 0995.93033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.