Abstract
The series connection \Sigma_{12} linear time-invariant systems \Sigma_1 and \Sigma_2 that have minimal state space system descriptions is considered. From these descriptions strict system equivalent polynomial matrix system descriptions in the manner of Rosenbrock are derived. They are based on the factorization of the transfer matrix of the subsystems as a ratio of two right or left coprime polynomial matrices. They give rise to a simple polynomial matrix system description of the tandem connection \Sima_{12} . Theorem 1 states that for the complete controllability and observability of the state space system description of \Sigma_12 it is necessary and sufficient that certain denominator and numerator groups are coprime. Consequences for feedback systems are drawn in Corollary 1. The role of pole-zero cancellations is explained by Lemma 3 and Corollaries 2 and 3.
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