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\(H_\infty \) control for nonlinear time-varying delay systems with convex polytopic uncertainties. (English) Zbl 1189.93041
Summary: This paper investigates \(H_\infty \) control for a class of nonlinear systems with time-varying delays and convex polytopic uncertainties. A new type of parameter-dependent Lyapunov-Krasovskii functional is introduced to derive delay-dependent sufficient conditions for the \(H_\infty \) optimal control with exponential stability. All the conditions developed in this paper are formulated in terms of linear matrix inequalities. Finally, a numerical example shows the effectiveness of the proposed methodology.

MSC:
93B36 \(H^\infty\)-control
93C20 Control/observation systems governed by partial differential equations
93C41 Control/observation systems with incomplete information
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
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