Although the stability of neural networks has been studied by many authors, the problem of stochastic effects on the stability has not been investigated until recently by Liao and Mao [7, 8]. In this paper we shall investigate the stability problem for stochastic neural networks with time-varying delay. The main technique employed in this paper is the well-known Razumikhin argument, which is co...

We present Lyapunov stability and asymptotic theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin methods. Our results apply to DDEs with multiple discrete delays, which may be nonautonomous the result, but autonomous (or periodically forced) result. main technique is replace DDE by a ordinary equation (ODE) where delayed t...

This paper introduces a new approach to the uniform practical stability theory of descriptor systems with infinite time delays in terms of two measurements. An easy-to-test criterion of uniform practical stability is given via Lyapunov functionals and Razumikhin technique. Finally, the application of the results obtained is demonstrated through an analysis of a class of descriptor systems with ...

The synchronization problem for a class of fractional-order complex dynamical networks with and without time-varying delay is investigated in this paper. By utilizing generalized Barbalat’s lemma, Razumikhin-type stability theory and matrix inequality technique, some sufficient criteria ensuring synchronization under pinning control and pinning adaptive feedback control are derived. Finally, th...

The main aim of this paper is to investigate the exponential stability of stochastic functional differential equations with Markovian switching. The Razumikhin argument and the generalized Itô formula will play their important roles in this paper. Applying our new results to several important types of equations e.g. stochastic differential delay equations and stochastic differential equations, ...

In this paper, we introduce the notion of stability sets for reaction-diffusion Cohen–Grossberg neural networks with time-varying delays. The Lyapunov–Razumikhin technique and a comparison principle are adapted to prove new criteria. addition, obtained results extended uncertain case, robust is also investigated. Examples considered demonstrate effectiveness our results.

In this paper, to concern the delay-dependent stability criterion, we adopt the integral inequality lemma on the LR method. Some variables are introduced to relax the integral term that is generated by the integral inequality lemma. Actually, the form of the criterion shows that, without any model transformations, we can obtain a stability criterion that can be extended to the stabilization pro...

In this paper, the exponential stability is investigated for a class of BAM neural networks with distributed delays and nonlinear impulsive operators. By using Lyapunov functions and applying the Razumikhin technique, delay–independent sufficient conditions ensuring the global exponential stability of equilibrium points are derived. These results can easily be utilized to design and verify glob...

In this work characterizations of external notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin functions of (uniform) Weighted Input-to-Output Stability are given. The results of this work have been developed for systems with outputs in abstract no...