Exponential Stability and Stabilization of Stochastic Neural Network Systems via Switching and Impulsive Control

The exponential stability and stabilization problem of stochastic neural network systems via a switching and impulsive control are dealt with in the chapter. To achieve the desired performance, a new type of switching and impulsive controllers are designed. With comparison to the previous results, the main characteristics of our proposed controller lies in the asynchronous behavior between switchings and impulses. That is, the occurrence instants of switchings and impulses are not the same. To describe the generation mechanisms of switchings and impulses, the concepts of dwell time and impulsive interval are employed. Then, based on multiple Lyapunov functions approach, sufficient conditions for mean square exponential stability are first established in terms of linear matrix inequalities (LMIs), based on which gain matrices of switching and impulsive controllers are presented. We, at last, provide two numerical examples to verify the applicability of the proposed theoretical results.

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