Robust control for a class of uncertain state-delayed singularly perturbed systems

Abstract This paper considers the problem of robust control for a class of uncertain state-delayed singularly perturbed systems with norm-bounded nonlinear uncertainties. The system under consideration involves state time delay and norm-bounded nonlinear uncertainties in the slow state variable. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all e ∈ (0, ∞) and independently of the time delay. Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed. We present an illustrative example to demonstrate the applicability of the proposed design approach.

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