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Robust sampled-data H∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals

In this paper, the problem of robust sampled-data H∞ control of linear uncertain singularly perturbed systems is investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Two types of controller design are considered: (1) with a fast sampling in the fast state and a slow one in the slow state, and (2) with a fast sampling in both states. For each type, a time-dependent Lyapunov functional associated with the sampling pattern is introduced to analyse the exponential stability and L2-gain performance of the closed-loop system. Linear matrix inequalities based solutions of the robust sampled-data H∞ control problem are derived. The new results are proved theoretically to be less conservative than the existing results. An illustrative example is given which substantiates the usefulness of the proposed method.