Fixed/predefined-time stability and designing of terminal sliding mode control of impulsive dynamical systems

Arnab Mapui, Md Arzoo Jamal and Santwana Mukhopadhyay

International Journal of Systems Science, 2025, vol. 56, issue 1, 139-156

Abstract: The contribution of the present work is two-fold. Firstly, some results on the predefined and fixed-time stability of non-linear impulsive systems are derived. Impulse-dependent sufficient conditions are derived for predefined-time estimation of settling-time under the influence of stabilising impulses. In contrast, a fixed-time estimate of the settling-time is obtained for destabilising impulses. Secondly, terminal sliding mode (TSM) control is designed in the presence of hybrid (continuous and impulsive) matched disturbances for n-dimensional systems. It shows that the trajectories can reach the sliding surfaces in fixed-time and thus will stay on it after that under the influence of the proposed TSM. Thus, the system states will converge to the origin in a fixed-time. Finally, three examples, which also consist of the stability of Cohen-Grossberg BAM neural networks, are provided to justify the proposed results numerically.

Date: 2025
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DOI: 10.1080/00207721.2024.2388809

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