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...

In this paper we study the stochastic stability properties of certain networked control system. Specifically we study the stability of the Model-Based Network Control System introduced in [9] under time-varying communication. The Model-Based Network Control System uses knowledge of the plant to reduce the number of packet exchanges and thus the network traffic. Stability conditions for constant...

We are concerned about the stochastic nonlinear delay differential equation. The stochasticity arises from white Gaussian noise, which is time derivative of standard Brownian motion. main objective this paper to introduce a new technique using Lyapunov functional for study stability zero solution system. Constructing appropriate deterministic system in neighborhood origin an effective way inves...

In this paper, we study the mean square stability of solution and its stochastic theta scheme for following differential equations driven by fractional Brownian motion with Hurst parameter H ? ( 1 2 , ) : d X t = f + g B . Firstly, consider special case when ? ? ? ? Secondly, nonlinear is studied. Due to presence long memory, even problem in sense has not been well studied, let alone numerical ...

Convergence, consistency, stability and pathwise positivity of balanced Milstein methods for numerical integration of ordinary stochastic differential equations (SDEs) are discussed. This family of numerical methods represents a class of highly efficient linear-implicit schemes which generate mean square converging numerical approximations with qualitative improvements and global rate 1.0 of me...

Positive results are proved here about the ability of numerical simulations to reproduce the exponentialmean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step si...

This paper studies a stochastic age-dependent competitive population system with diffusion. The definition of exponential mean square stability of numerical method is introduced. It is proved that the Euler scheme is exponentially stable in mean square sense under the given conditions. An example is given for illustration.