Lyapunov stability of differential inclusions with Lipschitz Cusco perturbations of maximal monotone operators

TL;DR

This paper establishes criteria for invariant sets and Lyapunov functions in differential inclusions with Lipschitz Cusco perturbations of maximal monotone operators, providing data-dependent conditions.

Contribution

It introduces new criteria for invariance and Lyapunov functions specifically for systems with Lipschitz Cusco perturbations of maximal monotone operators.

Findings

Criteria for weak and strong invariant sets

Characterizations of strong Lyapunov functions

Conditions depend only on system data

Abstract

We give criteria for weak and strong invariant closed sets for differential inclusions given in $\mathbb{R}^{n}$ and governed by Lipschitz Cusco perturbations of maximal monotone operators. Correspondingly, we provide different characterizations for the\ associated strong Lyapunov functions. The resulting conditions only depend on the data of the system.