Control-Lyapunov functions for systems satisfying the conditions of the Jurdjevic-Quinn theorem

Frédéric F. Mazenc (1, 2) , Mickael Malisoff (3)

1 ASB - Analyse des Systèmes et Biométrie
2 MERE - Water Resource Modeling
3 Department of mathematics

For a broad class of nonlinear systems satisfying the Jurdjevic-Quinn conditions, we construct a family of smooth control-Lyapunov functions whose derivatives along the trajectories of the systems can be made negative definite by smooth control laws that are arbitrarily small in norm. We also design state feedbacks of arbitrarily small norm that render our systems integral-input-to-state stable to actuator errors.

Mots clés: NON LINEAR SYSTEM; LYAPUNOV FUNCTION; FEEDBACK; STABILITY; JURDJEVIC-QUINN THEOREM; CONTROL-LYAPUNOV FUNCTIONS; GLOBAL ASYMPTOTIC AND INTEGRAL-INPUT-TO-STATE STABILIZATION

Mots clés: AUTOMATIQUE; STABILITE

Domaines: Mathématiques [math]; Informatique [cs]

Frédéric F. Mazenc, Mickael Malisoff. Control-Lyapunov functions for systems satisfying the conditions of the Jurdjevic-Quinn theorem. 44. IEEE Conference on Decision and Control, and the European Control Conference, Dec 2005, Seville, Spain. ⟨10.1109/CDC.2005.1582908⟩. ⟨hal-02763990⟩