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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
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