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Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

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Abstract

This study investigates the global Mittag-Leffler stability (MLS) problem of the equilibrium point for a new fractional-order coupled system (FOCS) on a network without strong connectedness. In particular, an integer-order coupled system is extended into the FOCS on a complex network without strong connectedness. Based on the theory of asymptotically autonomous systems and graph theory, sufficient conditions are derived to ensure the existence, uniqueness, and global MLS of the solutions of this FOCS on a network. Finally, a numerical example is provided to demonstrate the validity and potential of the proposed method for studying the MLS of FOCSs.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61873071) and Shandong Provincial Natural Science Foundation (Grant No. ZR2019MF027).

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Correspondence to Yonggui Kao.

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Meng, X., Kao, Y., Karimi, H.R. et al. Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness. Sci. China Inf. Sci. 63, 132201 (2020). https://doi.org/10.1007/s11432-019-9946-6

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Keywords

  • global Mittag-Leffler stability
  • fractional-order
  • coupled system
  • connectedness