Robust Stability Analysis of Uncertain Neural Networks with Time-Varying Delay-A Linear Matrix Inequality Approach

Abstract

In this paper, we investigate the problem of robust stability for uncertain stochastic neural network systems with interval time-varying delay. By means of singular model transformation technique, special Lyapunov-Krasovskii functional approach, similar Leibniz-Newton formula and linear matrix inequality (LMI) concept, some new stability conditions are derived for above systems. There are three main parts concerning our research results. The first result is to propose both delay-independent and delay-dependent criteria for guaranteeing the asymptotic stability of stochastic switched Hopfield neural network systems with constant parameters and time delay. The second result is to present several new delay-dependent criteria for testing the mean-square exponential stability of stochastic cellular neural network systems with interval time-varying delay. The third result is to provide sufficient conditions for ensuring asymptotic stability of stochastic neural network systems with uncertain parameters and interval time-varying delay. In the results, we do not assume that the network's activation functions are with the property of sigmoid function. The purpose of introducing the singular model transformation is to improve the results on bounds of the inner product of two vectors. Our results do not need the solution of Lyapunov equation or Riccati equation. Compared with existing results in the literature, our method is shown to be superior to other ones. Numerical examples are given to demonstrate the effectiveness of the proposed approach. Besides, our approach can be also applied to the stability testing problem for large-scale stochastic neural network systems with uncertain parameters and time-varying delays.