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Inner-estimating domains of attraction for discrete-time non-polynomial systems with piecewise difference inclusions

Author

Listed:
  • Shijie Wang
  • Zhikun She
  • Quanyi Liang
  • Junjie Lu
  • Wenyuan Wu

Abstract

In this paper, we propose two successive heuristic iterative methods for inner-estimating domains of attraction for discrete-time non-polynomial systems. Firstly, we utilise a discrete-time fuzzy model to derive a piecewise difference inclusion for the discrete-time non-polynomial system. Then, an initial heuristic iterative method is presented to inner-estimate the domain of attraction as large as possible by first iteratively calculating common Lyapunov-like functions and then heuristically updating piecewise difference inclusions. Afterwards, the initial heuristic iterative method is further improved by piecewise Lyapunov-like functions, arriving at a refined heuristic iterative method. Especially, we introduce homotopy continuation method to decrease the computational complexity. At last, our methods are applied to three discrete-time non-polynomial examples with a brief discussion.

Suggested Citation

  • Shijie Wang & Zhikun She & Quanyi Liang & Junjie Lu & Wenyuan Wu, 2023. "Inner-estimating domains of attraction for discrete-time non-polynomial systems with piecewise difference inclusions," International Journal of Systems Science, Taylor & Francis Journals, vol. 54(2), pages 423-442, January.
    • Handle: RePEc:taf:tsysxx:v:54:y:2023:i:2:p:423-442
    DOI: 10.1080/00207721.2022.2127341
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