On the zeros of blocked time-invariant systems

This paper studies the zero properties of blocked linear systems resulting from blocking of linear time-invariant systems. The main idea is to establish a relation between the zero properties of blocked systems and the zero properties of their corresponding unblocked systems. In particular, it is shown that the blocked system has a zero if and only if the associated unblocked system has a zero. Furthermore, the zero properties of blocked systems under a generic setting i.e. a setting which parameter matrices A,B,C,D assume generic values, are examined. It is demonstrated that nonsquare blocked systems i.e. blocked systems with number of outputs unequal to the number of inputs, generically have no zeros; however, square blocked systems i.e. blocked systems with equal number of inputs and outputs, generically have only finite zeros and these finite zeros have geometric multiplicity one.