We investigate the long term behavior of solutions to a stochastic Volterra integro-differential equation with a fading memory; the fading memory is represented by using a decaying exponential convolution kernel. We give sufficient conditions for asymptotic mean square stability of the solution. In a similar spirit, we investigate the long term behavior of solutions to discrete analogues of the...

This Letter deals with the problem of delay-dependent robust exponential stability in mean square for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-varying delays. Based on Lyapunov–Krasovskii functional and the stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Because of intr...

In this paper, we address the dynamic output feedback control problem of continuous time active fault tolerant control system with Markovian parameters (AFTCSMP). We will first derive a necessary and sufficient condition for the exponential stability in the mean square of the AFTCSMP under a dynamic output feedback control, in terms of coupled matrix inequalities, and then we will give an LMI (...

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions the geometric Brownian motion with delay. The are written terms parameters explicit case decay. For decay, they easily resolvable numerically. analytical method is based on construction a Lyapunov functional (asymptotic decay) forward-backward estimate (exponential decay).

In this article, the mean square exponential synchronization of a class of impulsive coupled neural networks with time-varying delays and stochastic disturbances is investigated. The information transmission among the systems can be directed and lagged, that is, the coupling matrices are not needed to be symmetrical and there exist interconnection delays. The dynamical behaviors of the networks...

This paper is concerned with delay-dependent exponential stability analysis and stabilization for continuous-time T-S fuzzy Markovian jump systems with mode-dependent time-varying delay. By constructing a novel Lyapunov-Krasovskii functional and utilizing some advanced techniques, less conservative conditions are presented to guarantee the closed-loop system is mean-square exponentially stable....

This paper investigates the problem of local stabilization of Markov jump nonlinear quadratic systems. A method is presented for the synthesis of a static nonlinear quadratic state feedback control law that ensures the local exponential mean square stability of the zero equilibrium point of the closedloop system in some polytopic region of the state-space with a guaranteed region of stability i...

Our aim is to study under what conditions the exact and numerical solution (based on equidistant nonrandom partitions of integration time-intervals) to a stochastic differential delay equation (SDDE) share the property of mean-square exponential stability. Our approach is trying to avoid the use of Lyapunov functions or functionals. We show that under a global Lipschitz assumption an SDDE is ex...