A Lyapunov approach to the stability of stochastic time delay systems

Abstract

This paper investigates the stability analysis of time-delay systems influenced by perturbations from standard Brownian motion, random coefficients, or stochastic process-based functions. The primary focus is on mean-fourth stability and stochastic stability. Using tailored Lyapunov functions, we derive conditions necessary to ensure both mean-fourth stability and stability in probability. Furthermore, the study explores systems with randomly varying coefficients, providing new theoretical insights. These findings are supported through illustrative examples and stability region analysis.