Multiple $\psi$ -Type Stability and Its Robustness for Recurrent Neural Networks With Time-Varying Delays

Abstract

In this paper, the ψ -type stability and robustness of recurrent neural networks are investigated by using the differential inequality. By utilizing ψ -type functions combined with the inequality techniques, some sufficient conditions ensuring ψ -type stability and robustness are derived for linear neural networks with time-varying delays. Then, by choosing appropriate Lipschitz coefficient in subregion, some algebraic criteria of the multiple ψ -type stability and robust boundedness are established for the delayed neural networks with time-varying delays. For special cases, several criteria are also presented by selecting parameters with easy implementation. The derived results cover both ψ -type mono-stability and multiple ψ -type stability. In addition, these theoretical results contain exponential stability, polynomial stability, and μ -stability, and they also complement and extend some previous results. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed criteria.