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Finite-time non-fragile boundary feedback control for a class of nonlinear parabolic systems

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Abstract

In this paper, the finite-time non-fragile boundary feedback control problem is investigated for a class of nonlinear parabolic systems, where both the multiplicative and additive controller gain variations are considered to describe the actuator parameter perturbation. Non-fragile boundary control strategies are designed with respect to two controller gain variations via collocated or non-collocated boundary measurement, respectively. In light of the finite-time stability and Lyapunov-based techniques, some sufficient conditions are presented in terms of linear matrix inequalities such that the resulting closed-loop system is well-posedness and practically finite-time stable. Finally, numerical examples are given to verify the effectiveness of the proposed design method.

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Acknowledgements

The research was partially supported by the National Natural Science Foundation of China (No. 61573013, 61603286). The authors gratefully acknowledge the helpful comments and suggestions of the associate editor and anonymous reviewers, which have improved the presentation of this paper.

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  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Chengzhou Wei & Junmin Li

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  1. Chengzhou Wei
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  2. Junmin Li
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Correspondence to Junmin Li.

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Wei, C., Li, J. Finite-time non-fragile boundary feedback control for a class of nonlinear parabolic systems. Nonlinear Dyn 103, 2753–2768 (2021). https://doi.org/10.1007/s11071-021-06277-7

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