Realization of stochastic systems with exogenous inputs and subspace system identification methods

A stochastic realization theory for a discrete-time stationary process with an ex- ogenous input is developed by extending the classical CCA technique. Some stochastic subspace identification methods are derived by adapting the realization procedure to finite input-output data. Key Words-- Stochastic realization; exogenous inputs; canonical correlation anal- ysis; oblique projection; subspace identification