Identifiability of Multivariable Stochastic Systems from Second-Order Input-Output Statistics

The identifiability (structure detectability and consistent parameter estimation) of linear multivariable stochastic system from the "joint process" statistics for general closed-loop characteristics is considered. Necessary and sufficient conditions for the identifiability of classes of systems are proven. Experimental tests to verify the identifiability and the use of dithers which guarantee it when the feedback is unknown are discussed.