Stability Analysis of Discrete‐Time Stochastic Systems With Markov Switching and State‐Dependent Delay

ABSTRACT This article focuses on the p th moment exponential stability of discrete‐time Markov switched stochastic systems with state‐dependent delay. By using Razumikhin technique, and stochastic analysis techniques, the state‐dependent delay with randomness due to the randomness of the system state can be addressed. With the help of stationary distribution of Markov switching and multiple Lyapunov–Krasovskii functionals approach, an appropriate switching rule is designed and a novel theorem on discrete‐time Markov switched stochastic systems with state‐dependent delay is established. Different from the previous results, the Markov switched with partially unstable subsystems and the state‐dependent delay with randomness are considered in this article, which brings many differences to the stability analysis of the system compared to traditional stability analysis. Furthermore, an illustrative example is performed to illustrate the effectiveness of the main theory.