Stability analysis of recurrent neural networks with time-varying delay and disturbances via quadratic convex technique

In recent years, the stability of recurrent neural networks (RNNs) has been investigated extensively. It is well known that time delays and external disturbances may derail the stability of RNNs. This paper analyzes the stability of RNNs subject to time-varying delay and disturbances included within time-varying delay. Given a stable neural network, the problem to be explored is how the RNNs remain stable in the presence of delay and external disturbances included within delay. A delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) for RNNs with time-varying delay are derived from the proposed augmented simple Lyapunov-Krasovski function, by applying a second-order convex combination with the property of quadratic convex functions. Simulation results of illustrative numerical examples are also delineated to substantiate the theoretical results.