Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems

Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

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.

Keywords: Impulsive systems, switched systems, quadratic stabilization, robust stabilization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060425

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.