Stability Analysis Of Recurrent Neural Networks

Recurrent neural networks(RNNs), as a special case of nonlinear dynamical systems,have been developed and applied in many scientific areas such as pattern recognition,associative memory design and so on. Most of these applications are extremely dependent on the dynamic behaviors of the given neural networks, which means that we should require the equilibrium points of the recurrent neural networks to be stable. As we all know that time delays commonly exist in many real-world systems, and the presence of time delays may degrade performance of the systems. On the other hand, in the applications of RNNs,systems may be faced with sudden variations in their structures and parameters due to component breakdown, or the abrupt change of the environment. What is to say, the RNNs may have finite modes and jump from one mode to another one according to a certain regulation. Therefore, in this paper, we shall investigate the global asymptotic stability of delayed recurrent neural networks in Section 2, then we turn to investigate the exponential stability problems of recurrent neural networks with time-varying delays and Markovian switching in Section 3. Moreover, a corollary is given to demonstrate that our results can be applied in a wider range, and compared with the existing results, our methods are less conservative. In the proof of the paper, by constructing a novel Lyapunov functional which adequately uses the information of the time delays, a new exponential stability criterion is obtained in terms of a set of linear matrix inequalities(LMIs). In the proof of these theorems, convex analysis approach is adopted which effectively upgrades the stability analysis and significantly reduces the conservatism. Finally, a specific example was given to substantiate the effectiveness of the proposed methods.