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Robust Finite-Time Stability of Fractional Order Linear Time-Varying Impulsive Systems

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Abstract

This paper considers the robust finite-time stability (FTS) of fractional order linear time-varying impulsive systems. First, using the fractional order Lyapunov function and generalized Gronwall inequality, some sufficient conditions are given to verify the robust FTS of fractional order linear time-varying systems. Then, the concept of FTS is extended to fractional order impulsive systems. A sufficient condition is given to verify the robust FTS of fractional order linear time-varying impulsive systems by combining the method of average dwell time with fractional order Lyapunov function. Finally, two numerical examples are provided to illustrate the theoretical results.

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Acknowledgments

This work was supported by National Natural Science Foundations of China (11401248, 60974139), Natural Science Foundation of Guangdong Province, China (S2011040003733), and Science and technology project of Huizhou (2012P10). The authors would also like to thank the editor and the reviewers for their constructive comments and suggestions which improved the quality of the paper.

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  1. Department of Mathematics, Huizhou University, Huizhou, 516007, People’s Republic of China

    Guopei Chen & Ying Yang

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  1. Guopei Chen
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  2. Ying Yang
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Correspondence to Ying Yang.

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Chen, G., Yang, Y. Robust Finite-Time Stability of Fractional Order Linear Time-Varying Impulsive Systems. Circuits Syst Signal Process 34, 1325–1341 (2015). https://doi.org/10.1007/s00034-014-9899-x

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