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2 Archives of Control Sciences

2 2023

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Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems

Basdouri Imed, Kasmi Souad, Lerbet Jean

Archives of Control Sciences

2023

Vol. 33, No. 1

55--70

This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.

ℎ-Stability of set differential equations

Boukthir Sihem, Ghanmi Boulbaba, Basdouri Imed, Ichalal Dalil, Lerbet Jean

Archives of Control Sciences

2023

Vol. 33, No. 4

761--788

In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems.