On the Generalization of Logarithmic Upper Function for Solution of a Linear Stochastic Differential Equation with a Nonexponentially Stable Matrix

Abstract

The problem of finding the upper function for the squared norm of the solution of a linear stochastic differential equation with a nonexponentially stable matrix is solved. A novel characteristic of a nonconstant stability rate of the matrix is introduced. The determined upper function generalizes the previously known logarithmic estimate and is expressed in closed form in terms of the rate of matrix stability. Examples of determining the upper function for different stability rates are provided.