Recurrence formulas are developed for finding mean, variances, and oth
er statistics of the state vector of linear systems with random time d
elay and Gaussian white noise input. These statistics are used to defi
ne optimal control functions for these systems. Lyapunov exponents are
used to evaluate the stability of the stationary solution when the co
ntrol algorithm is based on the stationary statistics of the state vec
tor. Two numerical examples are presented to illustrate the determinat
ion of the optimal control function and of the conditions required for
the existence of the stationary solution for systems with random time
delay. (C) 1997 Elsevier Science Ltd.