Abstract :
A criterion which guarantees complete controllability and complete observability of linear systems is derived. It is shown that if the output covariance of the system, when excited by stationary white noise, be separable and the components of the separating vectors be linearly independent, then the system is completely controllable and observable. This criterion is specially significant in designing shaping filters, or whitening filters when the only known information is the output covariance of the system.
