Advances in Difference Equations
Volume 2010 (2010), Article ID 278240, 14 pages
doi:10.1155/2010/278240
Research Article

Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems

Lamei Yan1 and Bin Liu2,3

1School of Printing Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
2Department of Information Engineering, The Australian National University, ACT 0200, Australia
3College of Science, Hunan University of Technology, Zhuzhou 412008, China

Received 14 September 2009; Accepted 16 April 2010

Academic Editor: Jianshe S. Yu

Copyright © 2010 Lamei Yan and Bin Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the problem of stabilization with optimal performance for dissipative DIHS (discrete-time impulsive hybrid systems). By using Lyapunov function method, conditions are derived under which the DIHS with zero inputs is GUAS (globally uniformly asymptotically stable). These GUAS results are used to design feedback control law such that a dissipative DIHS is asymptotically stabilized and the value of a hybrid performance functional can be minimized. For the case of linear DIHS with a quadratic supply rate and a quadratic storage function, sufficient and necessary conditions of dissipativity are expressed in matrix inequalities. And the corresponding conditions of optimal quadratic hybrid performance are established. Finally, one example is given to illustrate the results.