Kybernetika 62 no. 1, 99-114, 2026

β-exponential stability of time-delay systems based on sliding mode control

Nassim Athmouni, Nejib Brahmia, Tarek Fajraoui and Fehmi MabroukDOI: 10.14736/kyb-2026-1-0099

Abstract:

This paper investigates sliding mode control for one-sided Lipschitz non-linear systems with time-delays and uncertainties. A suitable integral sliding surface is introduced, explicitly accounting for delay terms and distinguishing itself from existing approaches. To guarantee the $\beta$-exponential stability, a new sufficient condition is derived in the form of a linear matrix inequality. Furthermore, an appropriate sliding mode control law is developed to enforce finite-time convergence of the system states to the sliding surface and guarantee their persistence on it. {Finally, a comparative numerical example is conducted to evaluate the performance and practicality of the proposed control strategy.}

Keywords:

sliding mode control, linear matrix inequality, time-delay systems, $\beta $-exponentially stable, one-sided Lipschitz

Classification:

93D05, 93D15, 93D23

paper.pdf

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