Invariant zeros of linear systems connected in series (Q1190632)

The first main result gives a precise relation between the invariant zeros of a system \(\Sigma\) and its transmission zeros in terms of a basis of the state space that is canonical with respect to reachability and observability. Here \(\Sigma\) is a finite-dimensional linear time invariant system. Next the authors consider the series connection of two systems \(\Sigma_ 1\) and \(\Sigma_ 2\) as above. Their next main result deals with the invariant and transmission zeros of \(\Sigma_ 1\Sigma_ 2\) in relation with the zeros of \(\Sigma_ 1\) and \(\Sigma_ 2\). Again the canonical state space bases play an important role. In their concluding remarks the authors refer to similar results obtained by them for linear periodic discrete-time systems.