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

Shijie Wang, Zhikun She, Quanyi Liang, Junjie Lu and Wenyuan Wu

International Journal of Systems Science, 2023, vol. 54, issue 2, 423-442

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.

Date: 2023
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DOI: 10.1080/00207721.2022.2127341

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