Comrade matrix and systems excited by colored noise

Stable linear systems described by state variable equations are considered where the input process is stationary and, in general, nonwhite. We show that there exists a natural coordinate basis for the system, the main properties for which imply that the state covariance matrix is a multiple of the identity, the system matrix itself is a comrade matrix, and the orthonormal polynomial set used to define the comrade matrix is obtained from the input spectrum and the system characteristic polynomial.