Stability Analysis For Switched Neural Networks

Switched neural networks, as a new type of neural networks model, have received great attention of researchers in recent years, because of the wide range of practical applications and theoretical significance. Because of the complexity of the discrete dynamic and the neural networks continuous dynamic, the stability problem of switched neural networks needs to be solved. Based on the theory of switched system, this paper analyzes stability and L2-gain stability of the switched neural networks, and designs the switching rule. The main contributions are as follows:The global asymptotic stability problem for switched Hopfield neural networks with time-varying delay under the hysteretic switching rule is considered in this paper. The single and multiple Lyapunov functions methods are employed to design the hysteretic switching rule by using the current state and previous value of switching signal. Sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the stability of such system. Two examples illustrate the effectiveness of the proposed approaches.The exponential stability of uncertain switched Cohen-Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed in this paper. Sufficient conditions are obtained in terms of LMIs which guarantee the exponential stability of the switched Cohen-Grossberg neural networks under the switched rule with the average dwell time property. A class of novel Lyapunov function is constructed to make the conclusion less conservative.The perturbed switched neutral recurrent neural networks is investigated. Sufficient conditions are obtained based on average dwell time approach and linear matrix inequality technique to guarantee the exponential stability of switched recurrent neural networks without perturbation and the L2-gain stability of perturbed switched recurrent neural networks. An estimation of state decay can be obtained by corresponding LMIs. Augmented Lyapunov function is used to establish less conservative results.