An algebraic method to solve the minimal partial realization problem for matrix sequences

This paper is a generalization to matrix sequences of the method given in [7] to solve the minimal partial realization problem for scalar sequences. In part 1, we define the minimal (partial) realization problem for matrix sequences. In part 2, the block Hankel matrix based on the matrix sequence is decomposed and from this decomposition the solution of the minimal realization problem can be constructed which is the input-output canonical form of Beghelli and Guidorzi. In part 3, we use the decomposition of part 2 to develop an algebraic algorithm to give all solutions of the minimal partial realization problem in input-output canonical form, i.e., with the minimal number of parameters. Part 4 contains some examples.