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3 Archives of Control Sciences

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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.

Mittag-Leffler stability analysis of a class of homogeneous fractional systems

Fajraoui Tarek, Ghanmi Boulbaba, Mabrouk Fehmi, Omri Faouzi

Archives of Control Sciences

2021

Vol. 31, No. 2

401--415

In this paper,we start by the research of the existence of Lyapunov homogeneous function for a class of homogeneous fractional Systems, then we shall prove that local and global behaviors are the same. The uniform Mittag-Leffler stability of homogeneous fractional time-varying systems is studied. A numerical example is given to illustrate the efficiency of the obtained results.

Global rational stabilization of a class of nonlinear time-delay systems

Echi Nadhem, Ghanmi Boulbaba

Archives of Control Sciences

2019

Vol. 29, No. 2

259--278

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.