含扰动切换系统在异步切换下的镇定
Stabilization of Switched Systems with Perturbations under Asynchronous Switching

作者: 向伟铭 * , 肖承勇 :西南科技大学应用技术学院; 肖建 :西南交通大学电气工程学院;

关键词: 切换系统异步切换镇定平均驻留时间扰动Switched Systems Asynchronous Switching Stabilization Average Dwell Time Perturbations

摘要: 本文研究了切换系统在异步切换下的镇定控制器设计问题。在控制器与控制对象的切换律失配情况下,通过分别讨论匹配时间段与不匹配时间段内控制器需要满足的约束条件,给出了基于平均驻留时间方法的镇定控制器设计方法。并将该方法推广到了含扰动的切换系统的镇定控制器设计方法中,设计的控制器在零扰动情况下能够保证闭环系统稳定,在非零扰动情况下能够保证系统状态有界。最后给出了仿真实例,验证了文中方法的有效性。

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

参考文献

[1] 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.

[2] 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.

[3] 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.

[4] 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.

[5] A. Balluchi, L. Benvenuti. Automotive engine control and hybrid systems: Challenges and opportunities. Proceedings of the IEEE, 2000, 88(7): 888-912.

[6] H. Sun, J. Zhao. Control Lyapunov functions for switched control systems. Proceedings of the American Control Con-ference, 2001, 3: 1890-1891.

[7] 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.

[8] 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.

[9] S. Pettersson. Synthesis of switched linear systems. Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, 5: 5283-5288.

[10] J. Malmborg, B. Bernhardsson, and K. J. Astrom. A stabilization switching scheme for multi-controller systems. 13th IFAC World Congress, 1996: 229-234.

[11] 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.

[12] 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.

[13] 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.

[14] 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.

[15] 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.

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