Abstract
A new method is developed for finding the mean and covariance functions of the transient response of a time-invariant stable linear system subject to a stationary Gaussian input. First, stationary response statistics are determined. Then, properties of conditional Gaussian random variables and processes are used to characterize the transient response of the system. The method can be applied to the analysis of linear systems subject to white/colored Gaussian inputs and deterministic/random initial conditions. Several examples are used to demonstrate the method of analysis.
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