Finite-time stability in probability of stochastic delay systems via generalized Halanay inequality

This paper presents novel advancements in the analysis and control of stochastic systems with time-varying delays, focusing on the concept of finite-time stability. Firstly, a new kind of generalized Halanay inequality is established. With this crucial approach, two essential stochastic Lyapunov theorems on the finite-time stability in probability of stochastic delay systems with bounded time delays and unbounded time delays, respectively, are derived. In addition, upper bound estimate for the stochastic settling time is given. Furthermore, a type of nonlinear stochastic delay systems is investigated and a delay-independent controller is proposed to achieve finite-time stability in probability. The effectiveness of the results is demonstrated through two illustrative examples.