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.
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.