Global stochastic stability analysis for stochastic neural networks with infinite delay and Markovian switching

This paper focuses on the stochastic stability for a novel kind of stochastic neural networks with infinite delay and Markovian switching. By using the Lyapunov method, stochastic analysis technique and M-matrix theory, some simple and easily testable sufficient conditions are presented to ensure the trivial solution is stochastically stable, stochastically asymptotically stable, and globally stochastically asymptotically stable, respectively. As a subsequent result, we develop the conditions that guarantee global stochastic asymptotic stability for stochastic neural networks with infinite delay, as well as global asymptotic stability for neural networks with infinite delay. From the perspective of theory, the derived stability criteria include some existing ones as its special cases, and are thus less conservative. Finally, two examples are given to demonstrate the applicability and effectiveness of the theoretical theorems.