Stabilization of Switched Systems with Perturbations under Asynchronous Switching
Abstract: In this paper, the stabilization of switched systems under asynchronous switching is investigated. When the controller mismatches the switching law, the stabilization condition for switched system during both matching and mismatching period is investigated and an approach of designing stabilizing controller for switched systems based on average dwell time is proposed, and then the approach is extended to design stabi-lizing controller for switched systems with perturbations. The designed controller guarantees the closed-loop system stable under the condition of vanishing perturbations, and ensures the closed-loop system bounded under the condition of non-vanishing perturbations. Finally, the simulation result shows that the approach proposed by this paper is effective.
文章引用: 向伟铭 , 肖建 , 肖承勇 (2011) 含扰动切换系统在异步切换下的镇定。 智能电网， 1， 11-16. doi: 10.12677/sg.2011.11003
 D. Leith, R. Shorten, and W. Leithead. Issue in the design of switched linear control systems: A benchmark study. International Journal of Adaptive Control, 2003, 17(2): 103-118.
 C. Sreekumar, V. Agar-wal. A hybrid control algorithm for voltage regulation in DC-DC boost converter. IEEE Transactions on Industrial Electronics, 2008, 55(6): 2530-2538.
 M. Song, T. J. Tarn, and N. Xi. Integration of task scheduling, action planning, and control in robotic manufacturing sys-tems. Proceedings of the IEEE, 2000, 88(7): 1097-1107.
 B. E. Bishop, M. W. Spong. Control of redundant manipulators using logic-based switching. Tampa, FL: Proceedings of the 37th IEEE Con-ference on Decision and Control, 1998: 16-18.
 A. Balluchi, L. Benvenuti. Automotive engine control and hybrid systems: Challenges and opportunities. Proceedings of the IEEE, 2000, 88(7): 888-912.
 H. Sun, J. Zhao. Control Lyapunov functions for switched control systems. Proceedings of the American Control Con-ference, 2001, 3: 1890-1891.
 H. Nael, P. D. El-Farra. Christofides. Feedback control of switched nonlinear systems using multiple Lyapunov functions. Proceedings of the American Control Conference, 2001, 5: 3496- 3502.
 J. Daafouz, P. Riedinger, and C. Lung. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach. IEEE Transactions on Auto-matic Control, 2002, 47(11): 1883-1887.
 S. Pettersson. Synthesis of switched linear systems. Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, 5: 5283-5288.
 J. Malmborg, B. Bernhardsson, and K. J. Astrom. A stabilization switching scheme for multi-controller systems. 13th IFAC World Congress, 1996: 229-234.
 L. Zhang, C. Wang, and L. Chen. Stability and stabili-zation of a class of multimode linear discrete-time systems with poly-topic uncertainties. IEEE Transactions on Industrial Electronics, 2009, 56(9), 3684-3692.
 向峥嵘, 向伟铭. 基于反步法的一类非线性切换系统控制器设计[J]. 控制与决策, 2007, 22(12): 1376-1380.
 L. Zhang, P. Shi. Stability, gain and asynchronous control of discrete-time switched systems with average dwell time. IEEE Transac-tions on Automatic Control, 2009, 54(9): 2193-2200.
 Z. Xiang, R. Wang. Robust control for uncertain switched nonlinear systems with time delay under asynchronous switching. IET Control Theory Appli-cations, 2008, 3(8): 1041-1050.
 J. P. Hespanha, D. Liberzon, and A. S. Morse. Stability of switched systems with average dwell time. 38th Conference on Decision and Control, 1999, 3: 2655-2660.