Stabilization with optimal performance for dissipative discrete-time impulsive hybrid systems

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.