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Robust fault detection for a class of uncertain switched nonlinear systems via the state updating approach. (English) Zbl 1291.93309
Summary: In this paper, the fault detection problem for a class of state-dependent switched nonlinear systems with linear switching surface is addressed. The investigation of fault detection problem includes two parts: design sub-filters for each subsystem, and determine a proper update of estimated state. A fault detection filter is proposed incorporating the update of the estimated state at switching instants and the multiple Lyapunov function approach is employed in the design process to reduce the conservativeness. It should be pointed out that the state update relation is derived based upon multiple Lyapunov functions and also on the information of switching surface. In the end, a special case in which the state space is divided into several polyhedral cells is discussed. A numerical example is given to illustrate the effectiveness of proposed results.

##### MSC:
 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93C10 Nonlinear systems in control theory
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##### References:
 [1] Liberzon, D., Switching in systems and control, (2003), Birkhauser Boston, MA · Zbl 1036.93001 [2] Sun, Z.; Ge, S. S., Switched linear systems—control and design, (2005), Springer-Verlag London, U.K. · Zbl 1075.93001 [3] Decarlo, R. A.; Branicky, M. S.; Pettersson, S.; Lennartson, B., Perspectives and results on the stability and stabilization of hybrid systems, IEEE Proc., 88, 1069-1082, (2000) [4] A. Balluchi, M.D. Benedetto, C. Pinello, C. Rossi, A. Sangiovanni-Vincentelli, Cut-off in engine control: a hybrid system approach, in: Proc. 36th IEEE Conf. Decision and Control, 1997, pp. 4720-4725. [5] B.E. Bishop, M.W. Spong, Control of redundant manipulators using logic-based switching, in: Proc. 36th IEEE Conf. Decision Control, 1998, pp. 16-18. [6] Zhang, W.; Branicky, M. S.; Phillips, S. M., Stability of networked control systems, IEEE Control Syst. Mag., 21, 84-99, (2001) [7] Castillo-Toledo, B.; Di Gennaro, S.; Loukianov, A. G.; Rivera, J., Hybrid control of induction motors via sampled closed representations, IEEE Trans. Ind. Electron., 55, 3758-3771, (2008) [8] Sreekumar, C.; Agarwal, V., A hybrid control algorithm for voltage regulation in DC-DC boost converter, IEEE Trans. Ind. Electron., 55, 2530-2538, (2008) [9] Narendra, K. S.; Balakrishnan, J. A., Common Lyapunov function for stable LTI systems with commuting $$A$$-matrices, IEEE Trans. Automat. Control, 39, 2469-2471, (1994) · Zbl 0825.93668 [10] Branicky, M. S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automat. Control, 43, 475-482, (1998) · Zbl 0904.93036 [11] Ye, H.; Michel, A. N.; Hou, L., Stability theory for hybrid dynamic systems, IEEE Trans. Automat. Control, 43, 461-474, (1998) · Zbl 0905.93024 [12] Zhang, L.; Wang, C.; Chen, L., Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties, IEEE Trans. Ind. Electron., 56, 3684-3692, (2009) [13] Morse, A. S., Supervisory control of families of linear set-point controllers, part 1: exact matching, IEEE Trans. Automat. Control, 41, 413-1431, (1996) · Zbl 0872.93009 [14] J.P. Hespanha, D. Liberzon, A.S. Morse, Stability of switched systems with average dwell time, in: Proc. 38th Conf. Decision Control, 1999, pp. 2655-2660. [15] Zhang, L.; Shi, P., Stability, $$L_2$$ gain and asynchronous control of discrete-time switched systems with average Dwell time, IEEE Trans. Automat. Control, 54, 2193-2200, (2009) [16] Lin, H.; Antsaklis, P. J., Stability and stabilizability of switched linear systems: a survey of recent results, IEEE Trans. Automat. Control, 54, 308-322, (2009) · Zbl 1367.93440 [17] Lunze, J.; Lamnabhi-Lagarrigue, F., Handbook of hybrid systems control: theory, tools, applications, (2009), Cambridge University Press New York [18] Patton, R. J., Fault detection and diagnosis in aerospace systems using analytical redundancy, Comput. Control Eng. J., 2, 127-139, (1991) [19] Himmelblau, D. M., Fault detection and diagnosis in chemical and petrochemical processes, (1978), Elsevier New York [20] Gertler, J. J.; Costin, M.; Fang, X.; Hira, R.; Kowalczuk, Z.; Luo, Q., Model-based on-board fault detection and diagnosis for automotive engines, Control Eng. Pract., 1, 3-17, (1993) [21] Li, X.; Zhou, K., A time domain approach to robust fault detection of linear time-varying systems, Automatica, 45, 94-102, (2009) · Zbl 1154.93341 [22] Ma, W.; Sznaier, M.; Lagoa, C., A risk adjusted approach to robust simultaneous fault detection and isolation, Automatica, 43, 499-504, (2007) · Zbl 1137.93370 [23] Zhong, M.; YE, H.; Shi, P.; Wang, G., Fault detection for Markovian jump systems, IET Control Theory Appl., 152, 397-402, (2005) [24] Zhao, Y.; Lam, J.; Gao, H., Fault detection for fuzzy systems with intermittent measurement, IEEE Trans. Fuzzy Syst., 17, 398-410, (2009) [25] Li, H.; Liu, H.; Gao, H.; Shi, P., Reliable fuzzy control for active suspension systems with actuator delay and fault, IEEE Trans. Fuzzy Syst., 20, 342-357, (2011) [26] Longhi, S.; Monteriu, A., Fault detection for linear periodic systems using a geometric approach, IEEE Trans. Automat. Control, 54, 1637-1643, (2009) · Zbl 1367.93629 [27] Yang, H.; Jiang, B.; Cocquempot, V., Fault tolerant control design for hybrid systems, (2010), Springer Verlag Berlin Heidelberg [28] Yang, H.; Jiang, B.; Cocquempot, V., A fault tolerant control framework for periodic switched nonlinear systems, Internat. J. Control, 82, 117-129, (2009) · Zbl 1154.93372 [29] Yang, H.; Jiang, B.; Cocquempot, V., Observer-based fault tolerant control for a class of hybrid impulsive systems, Internat. J. Robust Nonlinear Control, 20, 448-459, (2010) · Zbl 1298.93145 [30] Wu, L.; Lam, J., Weighted $$H_\infty$$ filtering of switched systems with time-varying delay: average Dwell time approach, Circuits Systems Signal Process., 28, 1017-1036, (2009) · Zbl 1191.94053 [31] Wu, L.; Shi, P.; Gao, H.; Wang, C., $$H_\infty$$ filtering for 2D Markovian jump systems, Automatica, 44, 1849-1858, (2008) · Zbl 1149.93346 [32] Wu, L.; Shi, P.; Gao, H., State estimation and sliding mode control of Markovian jump singular systems, IEEE Trans. Automat. Control, 55, 1213-1219, (2010) · Zbl 1368.93696 [33] Wu, L.; Ho, Daniel W. C., Reduced-order $$l_2 - l_\infty$$ filtering of switched nonlinear stochastic systems, IET Control Theory Appl., 3, 493-508, (2009) [34] Zhang, D.; Yu, L.; Zhang, W., Delay-dependent fault detection for switched linear systems with time-varying delays-the average Dwell time approach, Signal Process., 91, 832-840, (2011) · Zbl 1217.94081 [35] Xiang, W.; Xiao, J.; Iqbal, M. N., Fault detection for switched nonlinear systems under asynchronous switching, Internat. J. Control, 84, 1362-1376, (2011) · Zbl 1235.93245 [36] Xiang, W.; Xiao, J., $$H_\infty$$ filtering for switched nonlinear systems under asynchronous switching, Int. J. Syst. Sci., 42, 751-765, (2011) · Zbl 1233.93094 [37] Du, D.; Jiang, B.; Shi, P., Fault detection for discrete-time switched systems with intermittent measurements, Internat. J. Control, 85, 78-87, (2012) · Zbl 1282.93255 [38] Jiang, B.; Du, D.; Cocquempot, V., Fault detection for discrete-time switched systems with interval time-varying delays, Internat. J. Control, Autom. Syst., 9, 396-401, (2011) [39] Jiang, B.; Yang, H.; Cocquempot, V., Results and perspectives on fault tolerant control for a class of hybrid systems, Internat. J. Control, 84, 396-411, (2011) · Zbl 1222.93149 [40] H. Yang, B. Jiang, V. Cocquempot, Fault tolerant control in hybrid systems: a brief survey, in: Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes Barcelona, Spain, June 30-July 3, 2009, pp. 229-234. [41] M. Andersson, Object-oriented modeling and simulation of hybrid systems, Ph.D. dissertation, Dept. Automatic Control, Lund Inst. Tech., Lund, Sweden, Dec. 1994. [42] Johanssion, M.; Rantzer, A., Computation of piecewise quadratic Lyapunov functions for hybrid systems, IEEE Trans. Automat. Control, 43, 555-559, (1998) · Zbl 0905.93039 [43] Wu, L.; Zheng, W., Weighted $$H_\infty$$ model reduction for linear switched systems with time-varying delay, Automatica, 45, 186-193, (2009) · Zbl 1154.93326 [44] Wu, L.; Feng, Z.; Zheng, W., Exponential stability analysis for delayed neural networks with switching parameters: average Dwell time approach, IEEE Trans. Neural Netw., 21, 1396-1407, (2010) [45] Yao, X.; Wu, L.; Zheng, W., Fault detection filter design for Markovian jump singular systems with intermittent measurements, IEEE Trans. Signal Process., 59, 3099-3109, (2011) · Zbl 1392.94544 [46] Wu, L.; Ho, D. W.C.; Li, C. W., Sliding mode control of switched hybrid systems with stochastic perturbation, Systems Control Lett., 60, 531-539, (2011) · Zbl 1236.93038 [47] Xiang, W.; Xiao, J.; Iqbal, M. N., Robust finite-time bounded observer design for a class of uncertain non-linear Markovian jump systems, IMA J. Math. Control Inform., 29, 551-572, (2012) · Zbl 1256.93025 [48] Xiang, W.; Xiao, J.; Iqbal, M. N., Robust observer design for nonlinear uncertain switched systems under asynchronous switching, Nonlinear Anal. Hybrid Syst., 6, 754-773, (2012) · Zbl 1235.93053
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