Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay

doi:10.1007/s11424-022-1061-4

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (6): 2029-2045.DOI: 10.1007/s11424-022-1061-4

Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay

IMEN Akrouti¹, NADHEM Echi²

1. Faculty of Sciences of Gafsa, Department of Mathematics, Gafsa University, Zarroug Gafsa 2112, Tunisia;
2. Faculty of Sciences of Sfax, Department of Mathematics, Sfax University, BP 1171 Sfax 3000, Tunisia

Received:2021-03-04 Revised:2021-08-05 Online:2022-11-25 Published:2022-12-23
Contact: NADHEM Echi,Email:nadhemechi_fsg@yahoo.fr,nadhem.echi@fsgf.u-gafsa.tn

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IMEN Akrouti, NADHEM Echi. Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2029-2045.

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances. In case there is no perturbation, the exponential convergence of the observer was confirmed. When external disturbances appear in the system, a separation principle is established, and the authors show that the closed loop system is exponentially practical stable. By choosing a suitable Lyapunov-Krasovskii functional, the authors derive new sufficient conditions to guarantee the exponential stability of the systems. Finally, a physical model is performed to prove the efficiency and applicability of the suggested approach.

Key words: Lyapunov-Krasovskii, nonlinear time-delay systems, one-sided Lipschitz condition, separation principle

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