Kybernetika 62 no. 3, 546-559, 2026

Tighter settling-time bounds for fixed-time stable systems

Jiale Chen and Weigang SunDOI: 10.14736/kyb-2026-3-0546

Abstract:

This paper addresses the problem of refining settling-time upper-bound estimates for fixed-time stable systems under a three-term Lyapunov characterization. Without resorting to inequality-based techniques or special functions, a closed-form analytical upper bound for the settling-time function is derived using only elementary functions. Comparative analyses demonstrate that the proposed bound is tighter than existing results. The theoretical findings are further validated through the design of a fixed-time controller for a memristive neural network, with numerical simulations confirming the accuracy of the estimated settling time and the independence of the control scheme from initial conditions.

Keywords:

nonlinear systems, fixed-time stability, settling-time estimation, Lyapunov inequality, generalized homogeneity

Classification:

93C10, 93D40, 93D05

paper.pdf

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