On the almost-sure sample stability of systems with randomly time-varying delays

In a large class of multi-loop control systems, many feedback loops are “closed” through a time-shared digital computer, by means of algorithms which require information from sources which are sampled at a rate which is not synchronized with the sampling of the individual “plants”. This mis-synchronization, coupled with variations in the computer's task load caused by “interrupts”, results in a randomly time-varying delay in the closing of the various feedback loops. Consequently, the dynamics of each controlled “plant” in such a system may be modeled by means of a stochastic delay-differential equation. This paper presents some new research results concerning the sample stability, as opposed to statistical, or ensemble stability, of linear stochastic delay-differential equations.