Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.





References:
[1] S. B. Gershwin, Hierarchical flow control: A framework for scheduling
and planning discrete events in manufacturing systems, Proc. IEEE, 77
(1) (1989) 195-209.
[2] A. Gollu, P. P. Varaiya, Hybrid dynamical systems, in: Proc. 28th IEEE
Conf. Decision Control, Tampa, FL, Dec. 1989, pp. 3228-3234
[3] T. Yang, Impulsive systems and control: theory and applications, Nova,
New York, 2001.
[4] W. M. Haddad, V. Chellaboina, S. G. Nersesov, Impulsive and hybrid dynamical
systems: stability, dissipativity, and control, Princeton University
Press, Princeton, 2006.
[5] K.Wei, R. K. Yedavalli, Robust stabilizability for linear systems with both
parameter variation and unstructured uncertainty, IEEE Trans. Automat.
Contr., 34(2) (1989) 149-156.
[6] X. Li, C. E. Souza, Criteria for robust stability and stabilization of
uncertain linear system with state delay, Automatica, 33 (1997) 1657-
1662.
[7] X. Ding and H. Xu, Robust stability and stabilization of a class of
impulsive switched systems, Dyn. Contin. Discrete Impuls. Syst., 2 (2005)
795-798.
[8] D. D. Bainov, P. S. Simeonov, Systems with Impulse Effect: Stability,
Theory and Applications, Halsted Press, New York, 1989.
[9] I. R. Peterson, A stabilization algorithm for a class of uncertain linear
system, Syst. Control Lett., 8 (4) (1987) 351-357.
[10] K. Zhou, P. P. Khargonekar, Robust stabilization of linear systems with
norm bounded time-varying uncertainty, Syst. Control Lett., 10, (1988)
17-20.
[11] T. Shen, K. Tamura, Robust H1 control of an uncertain nonlinear
system via state feedback, IEEE Trans. Automat. Contr., 40 (1995, 1987)
766-768.
[12] H. Xu, X. Liu, K. L. Teo, Robust H1 stabilization with definite
attendance of uncertain impulsive switched systems, J. ANZIAM, 46 (4)
(2005) 471-484.
[13] I. R. Petersen, C. V. Hollot, A Riccati equation approach to the
stabilization of uncertain linear systems, Automatica, 22(4) (1986) 397-
411
[14] H. Xu, K. L. Teo, X. Liu, Robust stability analysis of guaranteed cost
control for impulsive switched systems, IEEE transactions on systems,
man, and cybernetics-part B, 38(5) (2008) 1419-1422.
[15] Z. H. Guan, D. J. Hill, X. M. Shen, On hybrid impulsive and switching
systems and application to nonlinear control, IEEE Trans. Autom.
Control, 50(7) (2005) 1058-1062.
[16] I. R. Petersen, C. V. Hollot, A Riccati equation approach to the
stabilization of uncertain linear systems, Automatica, 22 (4) (1986) 397-
411.
[17] L. Xie, C. E. Souza, RobustH1 control for linear time-invariant systems
with norm bounded uncertainty in the input matrix, Systems Control Lett.
14 (1990) 389-396.
[18] A. Packard, J. Doyle, Quadratic stability with real and complex perturbations,
IEEE Trans. Automat. Contr., 35 (2) (1990) 198-201.