Lyapunov-Krasovskii functionals for some classes of nonlinear time delay systems

TL;DR

This paper develops Lyapunov-Krasovskii functionals for analyzing nonlinear time delay systems with time-varying perturbations, providing new tools for stability and domain of attraction estimation.

Contribution

It introduces a novel Lyapunov-Krasovskii functional approach that aligns with Razumikhin conditions for nonlinear systems with delays.

Findings

Functional effectively estimates domain of attraction

Functional conditions match Razumikhin framework

Illustrative example demonstrates applicability

Abstract

In this contribution, we study an homogeneous class of nonlinear time delay systems with time-varying perturbations. Using the Lyapunov-Krasovskii approach, we introduce a functional that leads to perturbation conditions matching those obtained previously in the Razumikhin framework. The functionals are applied to the estimation of the domain of attraction and of the system solutions. An illustrative example is given.