Adaptive robust state stabilisation of uncertain non linear time-varying systems with delayed perturbation

Hizia Khelifa and Ines Ellouze

International Journal of Systems Science, 2021, vol. 52, issue 15, 3241-3253

Abstract: The problem of robust stabilisation for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown and an improved adaptation law with $ \sigma - $ σ−modification is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds, we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes in the presence of multiple delayed state perturbations is globally uniformly practically exponentially stable. Finally, a numerical example is given to demonstrate the validity of the results.

Date: 2021
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DOI: 10.1080/00207721.2021.1925374

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