Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching

Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching This paper investigates the problem of fault tolerant control of a class of uncertain switched nonlinear systems with time delay under asynchronous switching. The systems under consideration suffer from delayed switchings of the controller. First, a fault tolerant controller is proposed to guarantee exponentially stability of the switched systems with time delay. The dwell time approach is utilized for stability analysis and controller design. Then the proposed approach is extended to take into account switched time delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

[1]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[2]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[3]  N. El‐Farra,et al.  Robust predictive control of switched systems: Satisfying uncertain schedules subject to state and control constraints , 2008 .

[4]  Shouming Zhong,et al.  Delay-dependent stability of a type of linear switching systems with discrete and distributed time delays , 2008, Appl. Math. Comput..

[5]  Jamal Daafouz,et al.  Stability analysis for discrete time switched systems with temporary uncertain switching signal , 2007, 2007 46th IEEE Conference on Decision and Control.

[6]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[7]  Long Wang,et al.  Stabilization of switched linear systems with time-delay in detection of switching signal , 2005 .

[8]  Long-Yeu Chung,et al.  Robust reliable Hinfinity control for uncertain nonlinear systems via LMI approach , 2008, Appl. Math. Comput..

[9]  A. Morse,et al.  Nonlinear switched systems with state dependent dwell-time , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[11]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

[12]  Cunchen Gao,et al.  Output Variable Structure Control for Time-Invariant Linear Time-Delay Singular System , 2007, J. Syst. Sci. Complex..

[13]  Zhengrong Xiang,et al.  Robust control for uncertain switched non-linear systems with time delay under asynchronous switching , 2009 .

[14]  João Pedro Hespanha,et al.  Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle , 2004, IEEE Transactions on Automatic Control.

[15]  Li Yu,et al.  An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure , 2005, Appl. Math. Comput..

[16]  R. Brockett,et al.  Systems with finite communication bandwidth constraints. I. State estimation problems , 1997, IEEE Trans. Autom. Control..

[17]  Long Wang,et al.  Stabilization of Switched Linear Systems with Time-Varying Delay in Switching Occurrence Detection , 2007 .

[18]  David Angeli,et al.  Nonlinear norm-observability notions and stability of switched systems , 2005, IEEE Transactions on Automatic Control.

[19]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[20]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[21]  Zhang Lixian,et al.  Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems.* , 2007 .

[22]  Ximing Sun,et al.  Exponential stability for switched delay systems based on average dwell time technique and Lyapunov function method , 2006, 2006 American Control Conference.

[23]  Changlong Wang,et al.  Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[24]  Guan Haiwa,et al.  Delay-dependent robust stability and H∞ control for jump linear system with interval time-varying delay , 2006, 2007 Chinese Control Conference.

[25]  Zhengguo Li,et al.  Input-to-state stabilization of switched nonlinear systems , 2001, IEEE Trans. Autom. Control..

[26]  Wang Fu-zhong,et al.  LMI approach to reliable H ∞ control of linear systems , 2006 .

[27]  YUQIONG LIU,et al.  Reliable Control of Uncertain Nonlinear Systems , 1998, Autom..

[28]  Daizhan Cheng,et al.  STABILIZATION OF SWITCHED LINEAR SYSTEMS , 2008 .

[29]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[30]  Zhengrong Xiang,et al.  Robust L∞ reliable control for uncertain nonlinear switched systems with time delay , 2009, Appl. Math. Comput..

[31]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[32]  A. Stephen Morse,et al.  Switched nonlinear systems with state-dependent dwell-time , 2003, Syst. Control. Lett..

[33]  Man Liu,et al.  Reliable H∞ control for a class of switched nonlinear systems with actuator failures , 2007 .

[34]  Jun Zhao,et al.  GUARANTEED COST CONTROL FOR A CLASS OF UNCERTAIN SWITCHED DELAY SYSTEMS: AN AVERAGE DWELL-TIME METHOD , 2007, Cybern. Syst..

[35]  Hai Lin,et al.  Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[36]  Zhendong Sun.  A robust stabilizing law for switched linear systems , 2004 .

[37]  F. Sheikholeslam,et al.  Reliable H//sub/spl infin// control systems with uncertainties in all system matrices: an LMI approach , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[38]  Xinzhi Liu,et al.  Stability of switched systems with time delay , 2007 .