H∞H∞ model reduction for uncertain switched linear discrete-time systems

In this paper, the problem of H∞H∞ 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 H∞H∞ 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 an H∞H∞ 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.