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Parameter-dependent robust H∞ model reduction for discrete-time switched polytopic linear systems

This paper investigates the problem of parameter-dependent robust H∞ model reduction for a class of discrete-time switched linear systems with polytopic parameter uncertainties. The objective is to design a parameter-dependent homogeneous reduced-order switched system to approximate a given switched polytopic linear system such that the resulting error system is asymptotically stable with a guaranteed H∞ performance γ for any switching rules. Based on a switched parameter-dependent quadratic Lyapunov function (SPDQLF) combined with Finsler's lemma, a novel sufficient condition in terms of a set of linear matrix inequalities (LMIs) for robust H∞ performance analysis is first proposed and in turn the reduced-order models are synthesized. It is shown that by using a new linearization technique incorporating a bounding technique, the matrices for the reduced-order models can be obtained by solving a set of linear matrix inequalities, which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approaches.