On the Exponential Stability of Stochastic Perturbed Singular Systems in Mean Square

Abstract

The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic systems, in particular, of singular stochastic systems. The main objective of the paper is the analysis of the stability of stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. The uniform exponential stability in mean square and the practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems based on Lyapunov techniques are investigated. Moreover, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, an illustrative example is given to illustrate the effectiveness of the proposed results.

New stability criteria for stochastic perturbed singular systems in mean square

“…Remark 3.6. Here we should mention that in [12] we study the stability of the stochastic perturbed singular system for which its associated unperturbed system is a linear time-invariant singular system, where the corresponding matrix pencil is regular. Our main objective in this paper is to extend the results in [12] to the time-varying case where it is transferable into standard canonical form.…”

“…When the origin is not a trivial solution, we investigate the stability of the SDEs with respect to a small neighborhood of the origin. Several results on the stability of the nontrivial solution of stochastic systems proposed in [1,11,12].…”

“…To the best of our knowledge, no work has been published about the practical stability of linear time-varying stochastic perturbed singular systems. Our main objective in this paper is to extend the results in [12], which investigated the practical stability of linear time-invariant perturbed stochastic systems, to the case of linear time-varying stochastic perturbed systems.…”

Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion

“…In recent years, lots of results about stability have been reported in the literature [9,33]. For example, by applying Lyapunov techniques, Caraballo et al [3] analyzed the stability of a stochastic perturbed singular system under the assumption that the initial conditions are consistent. Marin et al [21] derived some results on stability and continuous dependence in Green-Naghdi thermoelasticity of Cosserat bodies.…”

“…Zong et al [40] investigated the asymptotic properties of systems represented by stochastic functional differential equations. In [3,9,22,33,40], G-Brownian motion has not been considered. In [38], the Markovian switching and the existence of the global unique solution have not been discussed.…”