# Stabilization of a collection of homogeneous single-input nonlinear systems

Wajdi Kallel, Thouraya Kharrat – GJM, Volume 5, Special Issue (2020), 37-43.

Simultaneous stabilization for a collection of single-input nonlinear homogeneous systems is dealt with in this paper. It is shown that any collection of nonlinear homogeneous systems can be simultaneously stabilized via a continuous homogeneous state feedback controller. We introduce some hypothesis for the desired systems on a submanifold of $\mathbb R^n$ diffeomorphic to $S^{n-1}$. An illustrative example is given to prove the efficiency of the method.

#### Milestones:

Accepted: February 06, 2020.
Published online: April 1st, 2020.

#### Authors:

Wajdi Kallel
Department of Mathematics, Faculty of Applied Sciences, Route
Umm Al-Qura University,21955 Mekkah, Saudi Arabia.
Faculté des sciences de Sfax, Département de Mathematiques, Route
Soukra Km 3.5, Sfax, Tunisia.
Thouraya Kharrat
Faculté des sciences de Sfax, Département de Mathématiques, Route Soukra Km 3.5, Sfax, Tunisia.