This paper considers the problem of quadratic mean-square stabilization of a class of stochastic linear systems using quantized state feedback. Different from the previous works where the system is restricted to be deterministic, we focus on stochastic systems with multiplicative noises in both the system matrix and the control input. A static quantizer is used in the feedback channel. It is sh...

We analyze impulsive systems with independent and identically distributed intervals between jumps. Our approach is based on a Volterra renewal-type equation that allows us to characterize the transitory and asymptotic behavior of the system. Necessary and sufficient conditions are given for mean square stability, stochastic stability and mean exponential stability, and the relation between the ...

Using an approach that has its origins in work of Halanay, we consider stability in mean square of numerical solutions obtained from the θ–Maruyama discretization of a test stochastic delay differential equation dX(t) = {f(t)− αX(t) + βX(t− τ )}dt+ {g(t) + η X(t) + μX(t− τ )} dW (t), interpreted in the Itô sense, where W (t) denotes a Wiener process. We focus on demonstrating that we may use te...

Keywords: Stochastic differential delay equation (SDDE) Split-step theta scheme Stochastic linear theta scheme Strong convergence rate Exponential mean square stability a b s t r a c t This paper establishes the boundedness, convergence and stability of the two classes of theta schemes, namely split-step theta (SST) scheme and stochastic linear theta (SLT) scheme, for stochastic differential de...

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponenti...

Large-time asymptotic properties of solutions to a class of semi-linear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponent...