Model Reduction for Switched Linear Discrete-Time Systems with polytopic uncertainties and arbitrary switching

Abstract

In this paper, the problem of H-infinity model reduction for switched linear discrete- time systems with polytopic uncertainties is investigated. A reduced-order switched model is constructed for a given robustly stable switched system, which has the same structural polytopic uncertainties as the original system such that the resulting error system is robustly asymptotically stable and an H1 error performance is guaranteed. A sufficient condition for the existence of the desired reduced-order model is derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem in such existence condition, the vertex system of reduced-order model can be obtained, which also provides a suboptimal H-infinity gain for the error system between the original system and the reduced-order model. A numerical example is given to show the effectiveness and the potential of the proposed techniques.