Characterization of infinite transmission zeros of state space systems

This paper deals with the characterization of infinite transmission zeros of linear, time-invariant state-space systems. For a square system (equal number of inputs and outputs), the number of infinite transmission zeros is given by the difference between the number of poles and the number of finite zeros. However, for systems with an unequal number of inputs and outputs, such a relationship does not hold. In this work, it is shown that the number of infinite transmission zeros is equal to the number of poles minus the maximum number of transmission zeros of the largest square subsystem. An algorithm is also provided to determine the number of infinite transmission zeros computationally