Nondecreasing Lyapunov functions

Michael Defoort (1) , Mohamed Djemai (1) , Stephan Trenn (2)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
2 Department of Mathematics University of Kaiserslautern

We propose the notion of nondecreasing Lyapunov functions which can be used to prove stability or other properties of the system in question. This notion is in particular useful in studying switched or hybrid systems. We illustrate the concept by a general construction of such a nondecreasing Lyapunov function for a class of planar hybrid systems. It is noted that this class encompasses switched systems for which no piecewise-quadratic (classical) Lyapunov function exists

Domaines: Automatique / Robotique

Michael Defoort, Mohamed Djemai, Stephan Trenn. Nondecreasing Lyapunov functions. 21st International Symposium on Mathematical Theory of Networks and Systems, Jul 2014, Groningen, Netherlands. ⟨hal-03469257⟩