Mean Square Stability of a Class of Closed-Loop Stochastic Systems

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...

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 Stability of Impulsive Stochastic Differential Systems

Mean-Square and Asymptotic Stability of the Stochastic Theta Method

Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?” We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the theta method. We extend some ...

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...