Mean-Square Stability Conditions for Linear Systems with Random Delays

In this paper we study stability properties of linear systems subject to random delays. We develop small-gain type mean-square stability conditions, by first obtaining small-gain mean-square robust stability conditions for systems containing multiplicative stochastic uncertainties and next, reformulating the random delay stability problem as one of robust stability against such uncertainties. The results allow us to determine stability using mean square criteria on the variances of the system under random delays, ascertaining whether the system's state variance matrix converges asymptotically to the zero matrix.