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

• Autorzy: Xiang Z. , Wang R. , Chen Q.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

time delay; fault tolerant control; switched nonlinear systems; asynchronous switching

PL

opóźnienie czasowe; sterowanie tolerujące uszkodzenia; układ komutowany; układ nieliniowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: Vol. 20, no 3
• Strony: 497--506
• Opis fizyczny: Bibliogr. 37 poz., rys., wykr.

Twórcy

autor

Xiang Z.

autor

Wang R.

autor

Chen Q.

• School of Automation Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China,

Bibliografia

• Abootalebi, A., Hossein Nia, S. and Sheikholeslam, F. (2005). Reliable H∞ control systems with uncertainties in all system matrices: An LMI approach, Proceedings of the 2005 IEEE Conference on Control Applications, Toronto, Canada, pp. 251-255.
• Boyd, S.P., Ghaoui, L.E., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
• Cheng, D., Guo, L., Lin, Y. andWang, Y. (2005). Stabilization of switched linear systems, IEEE Transactions on Automatic Control 50(5): 661-666.
• DePersis, C., De Santis, R. and Morse, A.S. (2002). Nonlinear switched systems with state dependent dwell-time, Proceedings of the 2002 IEEE Conference on Decision and Control, Las Vegas, NV, USA, pp. 4419-4424.
• DePersis, C., De Santis, R. and Morse, A.S. (2003). Switched nonlinear systems with state-dependent dwell-time, Systems and Control Letters 50(4): 291-302.
• Guan, H.W. and Gao, L.X. (2007). Delay-dependent robust stability and H∞ control for jump linear system with interval time-varying delay, Proceedings of the 26th Chinese Control Conference, Zhangjiajie, China, pp. 609-614.
• Guo, J.F. and Gao, C.C. (2007). Output variable structure control for time-invariant linear time-delay singular system, Journal of Systems Science and Complexity 20(3): 454-460.
• Gao, F.Y., Zhong, S.M. and Gao, X.Z. (2008). Delay-dependent stability of a type of linear switching systems with discrete and distributed time delays, Applied Mathematics and Computation 196(1): 24-39.
• Halanay, A. (1966). Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, NY.
• Hespanha, J.P. (2004). Uniform stability of switched linear systems: Extension of LaSalle's invariance principle, IEEE Transactions on Automatic Control 48(4): 470-482.
• Hespanha, J.P., Liberzon, D., Angeli, D. and Sontag, E.D. (2005). Nonlinear norm-observability notions and stability of switched systems, IEEE Transactions on Automatic Control 50(2): 154-168.
• Hetel, L., Daafouz, J. and Iung, C. (2007). Stability analysis for discrete time switched systems with temporary uncertain switching signal, Proceedings of the IEEE Conference on Decision and Control, New Orleans, LA, USA, pp. 5623-5628.
• Ji, Z., Guo, X., Xu, S. And Wang, L. (2007). Stabilization of switched linear systems with time-varying delay in switching occurrence detection, Circuits, Systems and Signal Processing 26(3): 361-367.
• Liberzon, D. (2003). Switching in Systems and Control, Birkhauser, Boston, MA.
• Lien, C.H., Yu, K.W., Lin, Y.F., Chung Y.J. and Chung, L.Y. (2008). Robust reliable H∞ control for uncertain nonlinear systems via LMI approach, Applied Mathematics and Computation 198(1): 453-462.
• Lin, H, Antsaklis, P.J. (2009). Stability and stabilizability of switched linear systems: A survey of recent results, IEEE Transactions on Automatic Control 54(2): 308-322.
• Liu, Y.Q.,Wang, J.L. and Yang, G.H. (1998). Reliable control of uncertain nonlinear systems, Automatica 34(7): 875-879.
• Mhaskar, P., El-Farra, N.H. and Christofides, P.D. (2008). Robust predictive control of switched systems: Satisfying uncertain schedules subject to state and control constraints, International Journal of Adaptive Control and Signal Processing 22(2): 161-179.
• Petersen, I.R. (1987). A stabilization algorithm for a class of uncertain linear systems, Systems and Control Letters 8(4): 351-357.
• Sun, X.M., Dimirovski, G.M., Zhao, J.,Wang,W. and Cyril, S.S. (2006a). Exponential stability for switched delay systems based on average dwell time technique and Lyapunov function method, Proceedings of the 2006 American Control Conference, Minneapolis, MN, USA, pp. 1539-1543.
• Sun, X.M., Zhao, J. and David, J.H. (2006b). Stability and L2-gain analysis for switched delay systems: A delaydependent method, Automatica 42(10): 1769-1774.
• Sun, Z. (2004). A robust stabilizing law for switched linear systems, International Journal of Control 77(4): 389-398.
• Sun, Z. (2006). Combined stabilizing strategies for switched linear systems, IEEE Transactions on Automatic Control 51(4): 666-674.
• Tomlin, C., Pappas, G.J., Sastry, S. (1998). Conflict resolution for air traffic management: A study in multiagent hybrid systems, IEEE Transactions on Automatic Control 43(4): 509-521.
• Varaiya, P. (1993). Smart cars on smart roads: Problems of control, IEEE Transactions on Automatic Control 38(2): 195-207.
• Wang, W. and Brockett, R.W. (1997). Systems with finite communication bandwidth constraints-Part I: State estimation problems, IEEE Transactions on Automatic Control 42(9): 1294-1299.
• Wang, R., Liu,M. and Zhao, J. (2007). ReliableH∞ control for a class of switched nonlinear systems with actuator failures, Nonlinear Analysis: Hybrid Systems 1(3): 317-325.
• Wang, R. and Zhao, J. (2007). Guaranteed cost control for a class of uncertain switched delay systems: An average dwell time method, Cybernetics and Systems 38(1): 105-122.
• Xiang, Z. and Wang, R. (2009a). Robust L∞ reliable control for uncertain nonlinear switched systems with time delay, Applied Mathematics and Computation 210(1): 202-210.
• Xiang, Z.R. and Wang, R.H. (2009b). Robust control for uncertain switched non-linear systems with time delay under asynchronous switching, IET Control Theory and Applications 3(8): 1041-1050.
• Xie, G. andWang, L.(2005). Stabilization of switched linear systems with time-delay in detection of switching signal, Applied Mathematics and Computation 305(6): 277-290.
• Xie, W., Wen, C. and Li, Z. (2001). Input-to-state stabilization of switched nonlinear systems, IEEE Transactions on Automatic Control 46(7): 1111-1116.
• Yao, B. and Wang, F.Z. (2006). LMI approach to reliable H∞ control of linear systems, Journal of Systems Engineering and Electronics 17(2): 381-386.
• Yu, L.(2005). An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure, Applied Mathematics and Computation 162 (3): 1325-1331.
• Zhai, G., Xu, X., Lin, H. and Liu, D. (2007). Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems, International Journal of Applied Mathematics and Computer Science 17(4): 447-454, DOI: 10.2478/v10006-007-0036-x.
• Zhang, L.X.,Wang, C.H. and Gao, H.J. (2007). Delay-dependent stability and stabilization of a class of linear switched time varying delay systems, Journal of Systems Engineering and Electronics 18(2): 320-326.
• Zhang, Y., Liu, X.Z. and Shen, X.M. (2007). Stability of switched systems with time delay, Nonlinear Analysis: Hybrid Systems 1(1): 44-58.