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Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT

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Abstract

This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.

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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

Authors
  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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Corresponding author

Correspondence to Leipo Liu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. U1404610, 61473115 and 61374077, Fundamental Research Project under Grant Nos. 142300410293, 142102210564 in the Science and Technology Department of Henan Province, the Science and Technology Research Key Project under Grant No. 14A413001 in the Education Department of Henan Province, and Young Key Teachers Plan of Henan Province under Grant No. 2016GGJS-056.

This paper was recommended for publication by Editor FENG Gang.

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Liu, L., Cao, X., Fu, Z. et al. Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT. J Syst Sci Complex 32, 857–874 (2019). https://doi.org/10.1007/s11424-018-7347-x

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  • DOI: https://doi.org/10.1007/s11424-018-7347-x

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