Abstract
SummaryIn this paper, an optimal guaranteed cost control strategy to stabilize discrete‐time linear parameter‐varying systems with bounded rates of variation is presented. Sufficient conditions for the synthesis of fixed gain and gain‐scheduled guaranteed cost controllers are given in terms of two sets of linear matrix inequalities. The main advantage of the proposed conditions is to rely on the use of homogeneous polynomial parameter‐dependent Lyapunov functions of arbitrary degree that allow to assess the stability of the closed‐loop system under the prescribed bound on the rate of parameter variations. In order to make the approach feasible, linear matrix inequality relaxations based on Pólya's theorem are addressed. Finally, the effectiveness of the proposed design methods is illustrated through numerical examples.
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