Differential Inclusions and Monotonicity Conditions for Nonsmooth Liapunov Functions

Abstract

In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the case of Lipschitz continuous functions and continuous di erential inclusions.

Cite this paper

@inproceedings{Bacciotti2000DifferentialIA, title={Differential Inclusions and Monotonicity Conditions for Nonsmooth Liapunov Functions}, author={Andrea Bacciotti and Francesca Ceragioli and Luisa Mazzi}, year={2000} }