Simultaneous stabilization of single-input nonlinear systems with bounded controls

Abderrahman Iggidr (1, 2) , Mohamed Oumoun (3, 4)

1 IECL - Institut Élie Cartan de Lorraine
2 Inria Nancy - Grand Est
3 UCA - Université Cadi Ayyad [Marrakech]
4 ENSA Marrakech - École nationale des sciences appliquées de Marrakech

In this paper, the simultaneous stabilization of single-input nonlinear systems with bounded controls is considered. Using the Lyapunov approach and based on Lin–Sontag’s formula for bounded and continuous stabilizers for affine nonlinear systems, a constructive universal formula for the bounded simultaneous stabilization of single-input nonlinear systems is presented explicitly. An illustrative example is given to demonstrate the validity of the method.

Mots clés: Simultaneous stabilization; nonlinear systems; control Lyapunov function; bounded state feedback

Domaines: Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]; Automatique / Robotique

Abderrahman Iggidr, Mohamed Oumoun. Simultaneous stabilization of single-input nonlinear systems with bounded controls. International Journal of Dynamics and Control, 2021, 9, pp.550-556. ⟨10.1007/s40435-020-00658-3⟩. ⟨hal-02943170⟩