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Robust \(H_\infty\) control for time-varying delay systems with nonlinear perturbation and polytopic uncertainty. (Chinese. English summary) Zbl 1313.93051

Summary: Robust \(H_\infty\) control problem of nonlinear systems with time-varying delay and polytopic uncertainty is discussed. The nonlinear condition satisfying a type of especial linear bound is assumed. By using the linear matrix inequality technique, a sufficient condition for nonlinear time-delay systems, which is asymptotically stable and satisfies \(H_\infty\) performance, is given, and the explicit design method of the robust \(H_\infty\) controller is obtained. Finally, a numerical example is supplied to clarify the feasibility and effectiveness of the proposed results.

MSC:

93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)
93D20 Asymptotic stability in control theory
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