Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays

Exponential Stability of Stochastic Differential Equation with Mixed Delay

“…By utilizing Doob's martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of SMDDE implies the almost surely exponentially stable. The obtained results generalize and improve some recent results (for instance, [19][20][21]). In particular, our theoretical results show that if SDE is exponentially stable and the time delay is sufficiently small, then the corresponding SMDDE will remain exponentially stable.…”

“…For example, Zhu and Song [19] obtained some exponential stability results for a class of impulsive nonlinear stochastic differential equations with mixed delays by Razumikhin technique, but these sufficient conditions only ensure the exponential stability of the trivial solution in the mean square and did not give a bound for the time delay . Deng et al [20] and L. Xu and D. Xu [21] focused on the corresponding study of exponential stability of neural network model. Thus, this paper aims to fill the gap in a sense.…”

New results on stability analysis for neutral stochastic linear system

“…Here, it should be mentioned that even if condition (3) holds, the methods proposed in [28,29] will encounter great difficulties while considering the stability for system (1). Although the free-weighting matrices technique utilised in [27,30] can discuss the robustly exponential stability in mean square moment for our concerned problem in this paper when μ i < 1 (i = 1, 2) are removed, some additional decisive variables and much more computational complexity can be brought.…”

“…The retarded-type delay means that the delay is in the states of systems, whereas the neutral-type delay means that the delay is in the derivatives of sates of systems. Since the existence of time-delay may lead to oscillation, divergence or instability [1,2], the stability of linear neutral system with delays has developed into a hot topic both in theory and in practice. At present, the stability results for linear neutral system with delays can be generally classified into two types: delay-independent one that can be applied to the delay with arbitrary size, and delay-dependent one that makes use of the size of the delay.…”

New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays

“…Therefore, noise will cannot be avoid in real applications of artificial neural networks. Practically, there are two main resources that degrade the performance of neural networks that is parameter uncertainties and stochastic perturbations [11]- [12]. In [13], pth moment exponential stochastic synchronization of coupled MNNs with mixed delays has been studied via delayed impulsive control.…”