Strict Lyapunov function constructions under LaSalle conditions with an application to Lotka-Volterra systems

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

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 L2S - Laboratoire des signaux et systèmes

We provide new techniques for building explicit global strict Lyapunov functions for broad classes of periodic time varying nonlinear systems satisfying LaSalle conditions. We illustrate our work using the Lotka-Volterra model, which plays a fundamental role in bioengineering. We use our strict Lyapunov constructions to prove robustness of the Lotka-Volterra tracking dynamics to uncertainty in the death rates.

Mots clés: PREDATOR PREY RELATION, LYAPUNOV FUNCTION, ROBUSTNESS, TIME VARYING SYSTEM, BIOLOGICAL SYSTEMS, LASALLE CONDITIONS

Mots clés: POPULATION DYNAMICS, LOTKA VOLTERRA MODEL, SYSTEME A PARAMETRE VARIABLE, MODELE LOTKA VOLTERRA

Domaines: Automatique; Automatique / Robotique

Michael Malisoff, Frédéric Mazenc. Strict Lyapunov function constructions under LaSalle conditions with an application to Lotka-Volterra systems. IEEE Transactions on Automatic Control, 2010, 55 (4), pp.841-854. ⟨10.1109/TAC.2010.2041995⟩. ⟨hal-00547797⟩