The covariance propagation equation including time-delayed inputs

The covariance propagation differential equation of a continuous linear dynamical system forced by a Gaussian purely random process is derived for the case when the inputs are related through time-delays. State variable formulation is used, a modified form of the well-known matrix differential equation is developed. The steady-state covariance equation is shown to be a "Lyapunov" type equation so that well-developed numerical techniques can be used for its solution.