Switching Law of a Three Second-order Linear Time Invariant Switched System

Main Article Content

Warinsinee Wattanapanich*
Thanasak Mouktonglang

Abstract

In this work, we study a problem of asymptotically stabilizing of a switched system, which consists of second-order linear time invariant subsystems. The subsystems used in this work have complex eigenvalues and two out of three subsystems cannot be stabilized. We then find a third subsystem and a new switching law that makes overall system asymptotically stabilizable. We propose a new sufficient condition on eigenvalues of the 3rd subsystem and a switching law that allows asymptotically stabilizable the overall switched system. A numerical example has been shown to guarantee the effectiveness of the proposed condition.


Keywords: Switched systems; Switching Law; Asymptotic stabilization


E-mail: warinsinee@hotmail.com

Article Details

Section
Original Research Articles

References

[1] Branicky, M.S., 1994, Stability of Switched and Hybrid Systems, In Proc. 33rd Conf. of Decision and control, pp 3498-3503.
[2] Branicky, M.S., 1998. Multiple Lyapunov Function and other analysis tools for switched and hybrid systems. IEEE Trans. on Automatic Control, vol 43, pp. 475-482.
[3] Liberzon, D. and Morse, A.S., Benchmark problems in stability and design of switched system, submitted to IEEE control systems magazine.
[4] Xu, X. and Antsaklis, P.J., 2000. Stabilization of second-order LTI switched system. Int. J.control, 73, 1261-1279.
[5] Hu, Bo., Zhai, Guisheng. and Michel, Anthony N. 2002. Hybrid static output feedback stabilization of second-order linear time-invariant systems. Linear Algebra and Its Application 351-352, 475-485.
[6] Zhang, Liguo., Chen, Yangzhou. and Cui, Pingyuan., 2005. Stabilization for a class of second-order switched system, Nonlinear Analysis (62)1527-1535.
[7] Plaat, Otto., 1971. Ordinary Differential Equation.California:University of San Francisco.
[8] Leon, Steven J., 2002. Linear Algebra with Applications, University of Massachusetts,Dartmouth.