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Finite-Time \(H_\infty \) Model Reference Control for Linear Systems Based on Average Dwell-Time Approach

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Abstract

This paper investigates the problem of state tracking for model reference control in a linear system with average dwell-time approach in a finite-time interval. Both matched and unmatched cases are taken into consideration in the system. The switching law is designed by the state error such that the considered tracking error is finite-time bounded and the considered system achieves a weighted \(H_\infty \) performance for the exogenous disturbance. With the aid of an error Lyapunov-like function and Schur complement lemma, the design of the switching law is formulated by linear matrix inequalities with sufficient conditions. A variable average dwell time is obtained that it is less than the traditional average dwell time in a finite-time interval. Finally, a numerical example is given to illustrate the effective design method of the switching law.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61503071), Natural Science Foundation of Jilin Province (20180520211JH) and Science Research of Education Department of Jilin Province (201693, JJKH20170106KJ).

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Authors and Affiliations

  1. School of Automation Engineering, Northeast Electric Power University, Jilin, 132012, Jilin, China

    Dongsheng Chen, Zhiqiang Wang & Qingyu Su

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  1. Dongsheng Chen
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  2. Zhiqiang Wang
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  3. Qingyu Su
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Correspondence to Qingyu Su.

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Chen, D., Wang, Z. & Su, Q. Finite-Time \(H_\infty \) Model Reference Control for Linear Systems Based on Average Dwell-Time Approach. Circuits Syst Signal Process 37, 4773–4788 (2018). https://doi.org/10.1007/s00034-018-0801-0

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  • DOI: https://doi.org/10.1007/s00034-018-0801-0

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