Uniqueness of minimal partial realizations and Markov parameter identification

The uniqueness of minimal partial realizations of input-output observations with elements in a Hilbert space is investigated. A sufficient condition and a necessary condition based on input-output data, without any assumptions on the state sequences, are derived. Under these conditions, models obtained by a class of identification schemes, known as “subspace methods”, are the unique minimal partial realizations. Markov parameter identification from input-output observations is studied. Balanced approximations for rapidly decaying systems can be obtained from this approach