This paper investigates the problem of designing ℋ ∞ robust output-feedback controllers for uncertain discrete-time linear systems with time-invariant parameters lying in polytopic domains. The computation procedure is based on linear matrix inequalities and is performed in two steps. The first stage designs a parameter-dependent state-feedback controller, that is used as an input parameter for the second stage, which synthesizes the desired robust ℋ ∞ output-feedback gain. The conditions are based on parameter-dependent Lyapunov functions and can deal with uncertainties in the output matrix of the system. Numerical examples illustrate the advantages of the proposed method when compared to other techniques available in the literature.
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Agulhari et al. (2010) studied this question.