The Asymptotical Stability Analysis for Switched Descriptor Systems

Abstract:

This paper is concerned with the asymptotical stability analysis for a class of switched uncertain descriptor systems with time-delay. The robustly asymptotical stability of this system is proven by making use of the generalized Lyapunov Stability theory, linear matrix inequality (LMI) tools and multiple Lyapunov function techniques. The conservation of result is greatly reduced by means of introducing the optimal weight matrix and avoiding vector matrix inequality in deducing procedure, in which there is no need of transformation and hypothesis for descriptor systems. The designed control law could surely make switched Descriptor Systems quickly approach the balanceable point. Experimentally, one numerical simulation verifies the effectiveness of this method.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 2150-2156
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.2150
• Online since: August 2010
• Authors: Wei Liu, Zi Yun Lu
• Keywords: Linear Matrix, Lyapunov Stability Theory, Switched Asymptotic Stability, Uncertain Descriptor Systems with Time-Delay

References

[1] Dai L. Singular Control Systems. New York: Springer-Verlag, (1989).

[2] Ishhara J Y, Terra M H. On the Lyapunov theorem for singular systems. IEEE Transactions on Automatic Control, 2002, 47(11): 1926-(1930).

DOI: 10.1109/tac.2002.804463

[3] Masubuchi I, Kamitane Y, Ohara A, Suda N, H control for descripytor systems: a matrix inequalities approach. Automatica, 1997, 33(4): 669-673.

DOI: 10.1016/s0005-1098(96)00193-8

[4] Savkin A V, Matveev A S. Cyclic linear differential automatica, 2000, 36(5): 727-734.

DOI: 10.1016/s0005-1098(99)00199-5

[5] Jeon D, Tomizuka M, Learning hybrid force and position control of robot manipulators. IEEE Transactions on Robotics and Automation, 1993, 9(4): 423-431.

DOI: 10.1109/70.246053

[6] Skafidas E, Evans R J, Savkin A V, Petersen I R. Stability results for switched controller systems, Automatica, 1999, 35(4): 553-564.

DOI: 10.1016/s0005-1098(98)00167-8

[7] Yin Yu-Juan, Zhao Jun. Stability of switched linear singular systems with impulsive effects. Acya Automatica Sinica, 2007, 33(4): 446-448.

[8] Liberzon D, Morse A S. Basic problemsin stability and design of switched and hybrid systems. IEEE Control Systems Magazine, 1999, 19(5): 59-70.

[9] Branicky M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 1998, 43(4): 475-482.

DOI: 10.1109/9.664150

[10] Zhao J, Dimirovski G M. Quadratic stability of a class of switched nonlinear systems. IEEE Transactions on Automatic Control, 2004, 49(4): 574-578.

DOI: 10.1109/tac.2004.825611

[11] Park P. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control, 1999, 44(4): 876-877.

DOI: 10.1109/9.754838

[12] Moon Y S, Park P, Kwon W H, Lee Y S. Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of control, 2001, 74(14): 1447-1455.

DOI: 10.1080/00207170110067116

[13] Fridman E, Shaked U. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control, 2002, 47(11): 1931-(1937).

DOI: 10.1109/tac.2002.804462

[14] Wu M, He Y, She J H, Liu G P. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 2004, 40(8): 1435-1439.

DOI: 10.1016/j.automatica.2004.03.004

[15] Xu S Y, James L. Improved delay-dependent stability criteria for time-delay systems. IEEE Transactions on Automatic Control, 2005, 50(3): 384-387.

DOI: 10.1109/tac.2005.843873

[16] Xu S Y, James L, Zou Y . New results on delay-dependent robust H∞control for systems with time-varying delay and parameter uncertainty. IEEE Transactions on Automatic Control, 2006, 42(2): 343-348.

[17] Xu S Y, Paul V D, Stefan R, James L. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Transactions on Automatic Control, 2002, 47(7): 1122-1128.

DOI: 10.1109/tac.2002.800651

[18] Xie L H. Output feedback H∞control of systems with parameter uncertainty. International journal of control, 1996, 63(4): 741-750.

DOI: 10.1080/00207179608921866