Control of time delay linear systems with Gaussian white noise

Recurrence formulas are developed for finding mean, variances, and other statistics of the state vector of linear systems with random time delay and Gaussian white noise input. These statistics are used to define optimal control functions for these systems. Lyapunov exponents are used to evaluate the stability of the stationary solution when the control algorithm is based on the stationary statistics of the state vector. Two numerical examples are presented to illustrate the determination of the optimal control function and of the conditions required for the existence of the stationary solution for systems with random time delay.