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Robust \(H _{\infty}\) control for uncertain singular systems with state delay. (English) Zbl 1039.93019

Summary: This paper addresses the problem of robust \(H_{\infty}\) control for uncertain continuous singular systems with state delay. The singular system under consideration involves state-time delay and time-invariant norm-bounded uncertainty. Based on the linear matrix inequality (LMI) approach, we design a memoryless state feedback controller law which guarantees that, for all admissible uncertainties, the resulting closed-loop system is not only regular, impulse free and stable, but also meets an \(H_{\infty}\)-norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the applicability of the proposed method.

MSC:

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
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