1. Adaptive robust state stabilisation of uncertain non linear time-varying systems with delayed perturbation.
- Author
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Khelifa, Hizia and Ellouze, Ines
- Subjects
- *
TIME-varying systems , *LINEAR systems , *STATE feedback (Feedback control systems) , *EXPONENTIAL stability , *ADAPTIVE control systems , *ROBUST control , *UNCERTAIN systems - 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 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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