New stability criteria for stochastic perturbed singular systems in mean square

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 Stability of Impulsive Stochastic Differential Systems

A new framework for Mean Square Stability of Stochastic Jump Linear Systems via Optimal Transport

In this paper, we provide a new framework for mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric which defines an optimal transport cost between probability density functions enables the stability analysis. Without any assumptions on the nature of the underlying jump process, the convergence of the Wasserstein distance guarantees the mean squar...

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...

Stochastic Stability of Singularly Perturbed Nonlinear Systems

The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the total stability type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for th...