Two Results for the Omega Limit Sets of Dynamical Systems

TL;DR

This paper presents two new results that allow for estimating omega limit sets of dynamical systems using less restrictive functions than traditional Lyapunov-based methods, broadening analytical tools.

Contribution

It introduces two novel results for omega limit sets that require weaker assumptions than classical Lyapunov and LaSalle theorems.

Findings

Omega limit sets can be estimated with less demanding functions.

New estimation methods extend classical Lyapunov techniques.

Results applicable to broader classes of dynamical systems.

Abstract

This paper provides two results for the omega limit sets of a dynamical system. We show that omega limit sets can be estimated by using functions that satisfy different (and in many cases less demanding) assumptions than the usual assumptions in Lyapunov theorems and LaSalle's theorem.