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Finite-Time Control of Uncertain Fractional-Order Positive Impulsive Switched Systems with Mode-Dependent Average Dwell Time

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Abstract

This paper is concerned with the problem of finite-time control of uncertain fractional-order positive impulsive switched systems (UFOPISS) via mode-dependent average dwell time (MDADT). The uncertainties refer to interval and polytopic uncertainties. Firstly, the proof of the positivity of UFOPISS is given. By constructing linear copositive Lyapunov functions, the finite-time stability (FTS) of autonomous system with MDADT is studied. Then, state feedback controllers are designed to guarantee the FTS of the resulting closed-loop system with interval and polytopic uncertainties, respectively. All presented conditions can be easily solved by linear programming. Finally, a fractional-order circuit model is employed to illustrate the effectiveness of the proposed method.

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Acknowledgements

The authors are grateful for the supports of the National Natural Science Foundation of China under Grants U1404610, 61473115 and 61374077, young key teachers plan of Henan province (2016GGJS-056).

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Authors and Affiliations

  1. School of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Leipo Liu, Xiangyang Cao, Zhumu Fu, Shuzhong Song & Hao Xing

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  1. Leipo Liu
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  2. Xiangyang Cao
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  3. Zhumu Fu
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  4. Shuzhong Song
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  5. Hao Xing
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Correspondence to Leipo Liu.

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Liu, L., Cao, X., Fu, Z. et al. Finite-Time Control of Uncertain Fractional-Order Positive Impulsive Switched Systems with Mode-Dependent Average Dwell Time. Circuits Syst Signal Process 37, 3739–3755 (2018). https://doi.org/10.1007/s00034-018-0752-5

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  • DOI: https://doi.org/10.1007/s00034-018-0752-5

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