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Lyapunov Stability Analysis for Incommensurate Nabla Fractional Order Systems

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Abstract

This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems. In particular, both Caputo definition and Riemann-Liouville definition are under consideration. With the convex assumption, several elementary fractional difference inequalities on Lyapunov functions are developed. According to the essential features of nabla fractional calculus, the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method. To substantiate the efficacy and effectiveness of the theoretical results, four examples are elaborated.

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Author information

Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, China

    Yiheng Wei & Xuan Zhao

  2. Department of Automation, University of Science and Technology of China, Hefei, 230026, China

    Yingdong Wei

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

    Yangquan Chen

Authors
  1. Yiheng Wei
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  2. Xuan Zhao
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  3. Yingdong Wei
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  4. Yangquan Chen
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Corresponding authors

Correspondence to Yiheng Wei, Xuan Zhao, Yingdong Wei or Yangquan Chen.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 62273092, the Science Climbing Project under Grant No. 4307012166, the Anhui Provincial Natural Science Foundation under Grant No. 1708085QF141, the Fundamental Research Funds for the Central Universities under Grant No. WK2100100028, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2016M602032 and the fund of China Scholarship Council under Grant No. 201806345002.

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Wei, Y., Zhao, X., Wei, Y. et al. Lyapunov Stability Analysis for Incommensurate Nabla Fractional Order Systems. J Syst Sci Complex 36, 555–576 (2023). https://doi.org/10.1007/s11424-023-1150-z

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  • DOI: https://doi.org/10.1007/s11424-023-1150-z

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