System zeros analysis via the Moore-Penrose pseudoinverse and SVD of the first nonzero Markov parameter

A new characterization of system zeros of an arbitrary linear system described by a state-space model S(A, B, C, D) is presented. The transmission zeros are characterized as invariant zeros of an appropriate strictly proper system with a smaller number of inputs and outputs than the original system. The approach is based on singular value decomposition (SVD) of the first nonzero Markov parameter. This result together with characterization of invariant and decoupling zeros, based on the Moore-Penrose inverse of the first nonzero Markov parameter and the Kalman canonical decomposition theorem, provided in the first part of the paper yield a complete characterization of system zeros of an arbitrary multi-input/multi-output system