Stability analysis of stochastic and random systems in the Lyapunov sense

Abstract

Lyapunov approach plays a vital role in addressing the issue of stability in deterministic and random (stochastic) systems. This paper is involved in the study of stability of linear and nonlinear systems perturbed by a standard Brownian motion, random coefficients or coefficient functions acting as stochastic processes. We mainly focus on the stability in mean-square and stochastic stability of these systems. Some suitable Lyapunov functions imply the necessary conditions of mean-square stability and stability in probability. Stability of systems with random variable coefficients are firstly discussed in this paper. The theoretical findings are supported by some examples with stability regions and some numerical simulations.

Keywords

• Random and stochastic systems
• Mean-square stability
• Lyapunov functions
• Stability analysis
• Brownian motion