How zeros appear in the Kalman canonical structure of MIMO discrete-time systems

A new approach to the question of determining and interpreting invariant zeros and zero directions in MIMO LTI discrete-time strictly proper and proper systems is presented. It is shown that invariant zeros of a strictly proper system appear as eigenvalues of an appropriate real matrix formed with the aid of the Moore-Penrose pseudoinverse of the first nonzero Markov parameter and of order equal to the dimension of the state space. The geometric structure of finite and infinite zeros as well as of state-zero and input-zero directions is described. An analogous discussion is carried out for proper systems. The Kalman canonical structure of the matrix containing invariant zeros is presented