Lyapunov Function Constructions for Slowly Time-Varying Systems

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

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

We provide general methods for explicitly constructing strict Lyapunov functions for general nonlinear slowly time-varying non-autonomous systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings using a perturbed friction model with slowly time-varying coefficients.

Mots clés: LYAPUNOV FUNCTION CONSTRUCTIONS; SLOWLY TIME-VARYING SYSTEMS; STABILITY ANALYSIS; INPUT-TO-STATE STABILITY; ANALYSE DE STABILITE

Mots clés: AUTOMATIQUE; VARIATION LENTE

Domaines: Mathématiques [math]; Informatique [cs]

Frédéric F. Mazenc, Michael Malisoff. Lyapunov Function Constructions for Slowly Time-Varying Systems. 45. IEEE Conference on decision and control, Dec 2006, San diego, United States. ⟨10.1109/CDC.2006.377292⟩. ⟨hal-02755241⟩