Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems
Dynamical Systems
2020-12-03 v1
Abstract
We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed and applications to hybrid dynamical systems are included.
Cite
@article{arxiv.2012.01097,
title = {Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems},
author = {Matteo Della Rossa and Rafal Goebel and Aneel Tanwani and Luca Zaccarian},
journal= {arXiv preprint arXiv:2012.01097},
year = {2020}
}
Comments
Mathematics of Control, Signals, and Systems, Springer Verlag, In press