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Stability analysis of switched fractional-order continuous-time systems

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Abstract

In this paper, a class of switched fractional-order continuous-time systems with order \(0<\alpha <1\) is investigated. First, an interesting property of fractional calculus is revealed, that is, unlike integer-order integral, it does not hold that \(_{t_{0}}D^{-\alpha }_{t}f(t)={_{t_{0}}}D^{-\alpha }_{t_1}f(t)+{_{t_{1}}}D^{-\alpha }_{t}f(t)\) for \(\alpha >0,~t_0<t_1<t\), not to mention fractional derivative. Then, a general formula of solutions for a piecewise-defined differential function with Caputo fractional derivative is introduced. After that, based on the derived equivalent solution of fractional-order piecewise-defined functions, the problem of finite-time stability for a class of switched fractional-order systems is reconsidered. Finally, two illustrative examples are provided to demonstrate the effectiveness of the presented sufficient conditions, respectively.

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Acknowledgements

This work was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2020JQ-402), by the Fundamental Research Funds for the Central Universities (Nos. GK201905001, GK201903004, 2019TS089) and also by the China Scholarship Council (No. 201806870032).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Tian Feng & Baowei Wu

  2. Institute of Mathematics, Jilin University, Changchun, 130012, China

    Lihong Guo

  3. School of Engineering, University of California, Merced, CA, 95348, USA

    YangQuan Chen

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  1. Tian Feng
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Correspondence to YangQuan Chen.

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Feng, T., Guo, L., Wu, B. et al. Stability analysis of switched fractional-order continuous-time systems. Nonlinear Dyn 102, 2467–2478 (2020). https://doi.org/10.1007/s11071-020-06074-8

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