On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type

Abstract

We consider the problem of mean-square stabilization of solutions of a system of linear deterministic difference equations with discrete time by perturbations of its coefficients by a stochastic “white-noise” process. The answer is negative and is based on the analysis of the corresponding matrix algebraic Sylvester equation introduced earlier by the author in the theory of stability of stochastic systems. At the same time, we answer the same question for a vector matrix system of linear difference equations with continuous time and for a vector matrix system of differential equations.