Delay-dependent exponential stability of recurrent neural networks with Markovian jumping parameters and proportional delays

Abstract

This paper deals with the global exponential stability problem of a class of recurrent neural networks with Markovian jumping parameters and proportional delays. Here the proportional delay is unbounded time-varying, which is different from unbounded distributed delay. The nonlinear transformation \(z(t)=x({\text {e}}^{t})\) transforms the recurrent neural networks with Markovian jumping parameters and proportional delays into the recurrent neural networks with Markovian jumping parameters, constant delays and variable coefficients. By constructing Lyapunov functional, a linear matrix inequality (LMI) approach is developed to establish a new delay-dependent global exponential stability sufficient condition in the mean square, which is related to the size of the proportional delay factor and can be easily checked by utilizing the numerically efficient MATLAB LMI toolbox, and no tuning of parameters is required. Two numerical examples and their simulations are given to illustrate the effectiveness of the obtained results.