Differential inclusions and quasi-Lyapunov functions

TL;DR

This paper establishes a sufficient condition for the existence of solutions to differential inclusions with bounded, possibly nonconvex values, and demonstrates its applicability through an example from optimal control theory.

Contribution

It introduces a new sufficient condition for solutions of differential inclusions with nonconvex values, extending existing theory and including an Olech-type result as a corollary.

Findings

Provides a sufficient condition for solution existence

Includes an Olech-type result as a corollary

Demonstrates applicability with an example from optimal control

Abstract

A sufficient condition for existence of a solution of a differential inclusion with a uniformly bounded right-hand side that has nonempty closed (possibly nonconvex) values is obtained. An Olech-type result is obtained as a corollary. An example, which originates from the Fuller problem from optimal control theory, is given to demonstrate the applicability of the main result.