Realization of invariant system descriptions from infinite Markov sequences

The realization of the infinite Markov sequence from the Hankel array for linear, constant, multidimensional systems is considered. It is shown that performing elementary operations directiy on the Hankel array yields both controllability and observability invariants as determined by Popov [9]. An efficient technique to extract these invariants under a change of basis in the state space is developed and an invariant system description under this transformation group is specified.