Stability of systems with nonlinear feedback through randomly time-varying delays

Abstract

In a large class of multi-loop control systems, many feedback loops are "closed" through a timeshared digital computer, using 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, in conjunction 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 resets concerning the sample stability (as opposed to statistical, or ensemble stability) of non-linear stochastic delay-differential equations.