Stability analysis of switched stochastic nonlinear functional systems

This article is concerned with stochastic finite time stability (SFTS) and stochastic fixed time stability (SFIXTS) of switched stochastic nonlinear functional systems. By using the Lyapunov–Razumikhin approach, stochastic analysis techniques, and stochastic process theory, several novel theorems on SFTS and SFIXTS are established. Concurrently, the estimations of stochastic settling time are given. Different from the previous general results, this article considers the effects of noise, time‐delays, and switches. The SFTS and SFIXTS conditions are established, which are quite different from the traditional exponential stability or almost sure stability. Furthermore, two examples are given to illustrate the effectiveness of the obtained results.