Filtering and fault estimation of descriptor switched systems

In this paper, the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to Lipschitz nonlinearities and unknown inputs (UI). The UI appear both on the dynamic and on the measurement equations. Two problems are addressed by L 2 -gain minimization with the use of switched Lyapunov functions and formulated by LMI. First, a functional observer for switched Lipschitz nonlinear descriptor system is proposed for robust state estimation. Second, fault estimation is performed by filtering the output estimation error, as usually done in the residual generation framework. Moreover, frequency weighting functions can be used to shape the response to the fault and thus improve the estimation.

[1]  M. Darouach,et al.  Stabilisation of Singular LPV Systems , 2008 .

[2]  Yuan Gong Sun,et al.  Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays , 2006, Appl. Math. Comput..

[3]  Stoyan Kamenov Kanev,et al.  Robust fault-tolerant control , 2004 .

[4]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[5]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[6]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[7]  Didier Georges,et al.  Robust fault-tolerant control for descriptor systems , 2004, IEEE Transactions on Automatic Control.

[8]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[9]  Guangming Xie,et al.  Delay-dependent robust stability and Hinfinity control for uncertain discrete-time switched systems with mode-dependent time delays , 2007, Appl. Math. Comput..

[10]  Mohamed Darouach,et al.  Robust admissibility of uncertain switched singular systems , 2011, Int. J. Control.

[11]  B. Marx,et al.  Hα-filtering and state feedback control for discrete-time switched descriptor systems , 2009 .

[12]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[13]  G. Millerioux,et al.  Unknown input observers for switched linear discrete time systems , 2004, Proceedings of the 2004 American Control Conference.

[14]  Nael H. Ei-Farra,et al.  Output feedback control of switched nonlinear systems using multiple Lyapunov functions , 2001 .

[15]  Steven X. Ding,et al.  Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems , 2007, Autom..

[16]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[17]  El Kebir Boukas,et al.  Stability and robust stabilization for uncertain discrete stochastic hybrid singular systems with time-delay , 2008, 2008 47th IEEE Conference on Decision and Control.

[18]  Ahmad Haidar,et al.  Robust stability criteria for Markovian jump singular systems with time-varying delays , 2008, 2008 47th IEEE Conference on Decision and Control.

[19]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[20]  Shengyuan Xu,et al.  Stabilization of discrete-time singular systems: a matrix inequalities approach , 1999, Autom..

[21]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[22]  Izumi Masubuchi,et al.  PII: S0005-1098(96)00193-8 , 2003 .

[23]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[24]  Damien Koenig,et al.  Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation , 2005, IEEE Transactions on Automatic Control.

[25]  Michel Kinnaert,et al.  Diagnosis and Fault-Tolerant Control , 2006 .

[26]  Damien Koenig,et al.  Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems , 2008, IEEE Transactions on Automatic Control.