Exponential mean square stability of partially linear stochastic systems

Exponential Stability in Mean Square for a General Class of Discrete-time Linear Stochastic Systems

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability...

Mean square exponential stability of stochastic delay cellular neural networks

The dynamical behaviors of stochastic neural networks have appeared as a novel subject of research and applications, such as optimization, control, and image processing(see [1-12]). Obviously, finding stability criteria for these neural networks becomes an attractive research problem of importance. Some well results have just appeared, for example, in [1-5], for stochastic delayed Hopfield neur...

A-stability and Stochastic Mean-square Stability∗

This note extends and interprets a result of Saito and Mitsui [SIAM J. Numer. Anal., 33 (1996), pp. 2254–2267] for a method of Milstein. The result concerns mean-square stability on a stochastic differential equation test problem with multiplicative noise. The numerical method reduces to the Theta Method on deterministic problems. Saito and Mitsui showed that the deterministic A-stability prope...

Mean square exponential and non-exponential asymptotic stability of impulsive stochastic Volterra equations

* Correspondence: [email protected] Department of mathematics, Shanghai Jiaotong University, Shanghai, 200240, China Full list of author information is available at the end of the article Abstract In this article, some inequalities on convolution equations are presented firstly. The mean square stability of the zero solution of the impulsive stochastic Volterra equation is studied by using ...

Mean Square Stability of Impulsive Stochastic Differential Systems