Stability Analysis Of Stochastic Differential Delay Systems

In this paper, the problem of stability for stochastic systems with time-delays is studied by using Lyapunov stability theory. We study the stability of tochastic systems with discrete and distributed time-varying delays, the mean square exponential stability of discrete-time stochastic systems with time-varying and the mean square exponential stability of discrete-time Markovian jumping systems with mode-dependent time delays. Some results obtained are improved and perfected. This paper mainly includes the following three parts:1. Investigate on the problem of the global exponential stability of stochastic neural networks with discrete and distributed time-varying delays and parameter uncertainties. Based on Lyapunov stability theory and stochastic approaches, delay-dependent criteria are derived to ensure the robust exponential stability in the mean square for the system A numerical example is given to illustrate the effectiveness of our result.2. We study the stability property of the mean square exponential stability is investigated for a class of discrete-time stochastic neural networks with time-varying and norm-bounded uncertainties by employing the inequality methods and establishing some suitable Laypunov-functional we obtain some much better stability criterias, finally one numerical example has given to demonstrate the effectiveness of our results.3. In this part, the mean square exponential stability is investigated for a class of discrete-time Markovian jumping neural networks with mode-dependent time delays .Based on Lyapunov stability theory and stochastic approaches, delay-dependent criteria are derived to ensure the robust exponential stability in the mean square for the addressed system. Meantime, an example is presented to show the usefulness of the derived LMI-based stability condition.