Stability of synchronization in coupled time-delay systems using Krasovskii-Lyapunov theory

TL;DR

This paper investigates the stability of synchronization in unidirectionally coupled time-delay systems using Krasovskii-Lyapunov theory, providing general stability conditions applicable even with time-dependent coefficients, supported by numerical simulations.

Contribution

It derives a unified stability condition for synchronization in time-delay systems using Krasovskii-Lyapunov theory, applicable to general cases with time-dependent coefficients.

Findings

Stability condition valid for various cases including time-dependent coefficients

Analytical results confirmed by numerical simulations

Applicable to general unidirectionally coupled time-delay systems

Abstract

Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general situation (but with a constraint) where all the coefficients of the error equation corresponding to the synchronization manifold are time-dependent. These analytical results are also confirmed by numerical simulation of paradigmatic examples.