H₂ Model Reduction Problems For Discrete-Time Switched Systems

In this paper,H₂ reduction model for discrete-time switched systems will be considered. For a given switched system,we focus on computing its H₂ reduced-order model such that the corresponding error system is exponentially stable and has a generalized H₂ perfbrmance index for certain useful class of switching signals with average dwell time.The paper is mainly divided into five sections.The first section is the introduction of the whole paper.We introduce the switched system,and talk about the research of the model reduction problem.The next section consisting of some definitions and theorems,mainly investigates the exponential stability and H₂ perfbrmance index of discrete-time switched systems.In the third section,based on some important lemmas and propositions,the existence conditions of the reduction model are derived and expressed in terms of linear matrix inequalities(LMIs).H₂ reduction model for discrete-time switched systems with polytopic uncertainty is investigated in the fourth section.At last,we summarize the results of the whole paper.