Robust Finite-Time H∞ Controller Design for Uncertain One-Sided Lipschitz Systems with Time-Delay and Input Amplitude Constraints
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This paper studies the finite-time stabilization of a class of time-delay nonlinear systems in the presence of uncertainties and external disturbances under the input amplitude constraints. The external disturbances are unknown and energy-bounded and the nonlinear vector function of system satisfies the one-sided Lipschitz condition which is less conservative than the well-known Lipschitz condition. To have a robust finite-time stabilization in the considered system, a robust H∞ controller is designed with respect to a finite-time interval. In this regard, two theorems are presented based on Lyapunov–Krasovskii approach and the sufficient conditions are derived as linear matrix inequalities which guarantee the finite-time boundedness of the resulting uncertain closed-loop system. The effectiveness of the proposed method is illustrated by two examples, one numerical and one practical (time-delay Chua’s circuit) with simulation results.
KeywordsNonlinear time-delay systems One-sided Lipschitz nonlinear function Finite-time boundedness (FTB) H∞ performance index Chua’s circuit Input amplitude constraint
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