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Nonfragile robust finite-time \(L_2-L_\infty\) controller design for a class of uncertain Lipschitz nonlinear systems with time-delays. (English) Zbl 1271.93051

Summary: The nonfragile robust finite-time \(L_2-L_\infty\) control problem for a class of nonlinear uncertain systems with uncertainties and time-delays is considered. The nonlinear parameters are considered to satisfy the Lipschitz conditions and the exogenous disturbances are unknown but energy bounded. By using the Lyapunov function approach, a sufficient condition for the existence of nonfragile robust finite-time \(L_2-L_\infty\) controller is given in terms of Linear Matrix Inequalities (LMIs). The finite-time controller is designed such that the resulting closed-loop system is finite-time bounded for all admissible uncertainties and satisfies the given \(L_2-L_\infty\) control index. Simulation results illustrate the validity of the proposed approach.

MSC:

93B35 Sensitivity (robustness)
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93B52 Feedback control
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