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Robust Finite-Time H∞ Controller Design for Uncertain One-Sided Lipschitz Systems with Time-Delay and Input Amplitude Constraints

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Abstract

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.

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  1. Department of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, P.O. Box 71555-313, Shiraz, Iran

    Hadi Gholami & Tahereh Binazadeh

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  1. Hadi Gholami
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  2. Tahereh Binazadeh
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Correspondence to Hadi Gholami or Tahereh Binazadeh.

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Gholami, H., Binazadeh, T. Robust Finite-Time H∞ Controller Design for Uncertain One-Sided Lipschitz Systems with Time-Delay and Input Amplitude Constraints. Circuits Syst Signal Process 38, 3020–3040 (2019). https://doi.org/10.1007/s00034-018-01018-5

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