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Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks

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Abstract

Lyapunov direct method provides a very effective approach to analyze stability of nonlinear systems. However, the well-known Leibniz rule is not suitable for fractional derivatives, which is the main reason that there are few analytical results on stability of fractional systems. This paper deals with stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks. Applying fractional Lyapunov direct method and S-procedure lemma, several sufficient conditions on stability and a simple condition on global synchronization of a class of fractional singular dynamical networks in terms of linear matrix inequalities are derived. Finally, two simple examples are given to show that our proposed methods are simple and convenient in computation.

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Acknowledgments

This research is supported by the National Natural Science Fund and Tianyuan Special Fund of China (11371027, 11326115, 11471015), Specialized Research Fund for the Doctoral Program of Higher Education of China (20133401120013), Natural Science Project of Colleges of Anhui Province (KJ2013A032) and Doctoral Starting and Outstanding Young Teacher Fund of Anhui University (023033190181, 023033050055, 023033010264).

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Song Liu, Xian-Feng Zhou, Xiaoyan Li & Wei Jiang

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  1. Song Liu
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  2. Xian-Feng Zhou
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  3. Xiaoyan Li
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  4. Wei Jiang
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Correspondence to Song Liu.

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Liu, S., Zhou, XF., Li, X. et al. Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks. Nonlinear Dyn 84, 2377–2385 (2016). https://doi.org/10.1007/s11071-016-2651-2

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  • DOI: https://doi.org/10.1007/s11071-016-2651-2

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