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${H}_{\infty }$ model reduction for uncertain switched linear discrete-time systems. (English) Zbl 1152.93321
Summary: The problem of ${H}_{\infty }$ 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 ${H}_{\infty }$ 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 ${H}_{\infty }$ 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.
##### MSC:
 93B11 System structure simplification 93B36 ${H}^{\infty }$-control 93D20 Asymptotic stability of control systems 93C55 Discrete-time control systems