H∞ Output-Feedback Gain-Scheduled Control for Discrete-Time Linear Systems Affected by Time-Varying Parameters

Abstract This paper deals with the problem of H ∞ reduced order dynamic output feedback control for discrete-time linear systems affected by time-varying parameters with polynomial dependency and norm-bounded terms. The main motivation comes from recent discretization methods for uncertain systems, that produce polynomially parameter-dependent discretized systems of arbitrary degree with norm-bounded terms. The design conditions are provided in terms of sufficient parameter-dependent LMI conditions combined with scalar searches, being capable to synthesize robust or gain-scheduled controllers. The approach is also particularized to handle the popular class of time-varying polytopic systems, having as novelty no requirement of special treatment for the output measured matrix. Numerical examples are provided to illustrate the potentialities of the approach to cope with discretized systems and the efficiency of the relaxations when compared with the existing methods for gain-scheduled or robust stabilization of polytopic time-invariant and time-varying systems.

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