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Stabilization of polynomial systems in ℝ3 via homogeneous feedback

Jerbi Hamadi, Kharrat Thouraya, Mabrouk Fehmi

Journal of Applied Analysis

2022

Vol. 28, nr 2

189--197

In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

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.