Equivalence of characterizations of fixed modes (Q1319480)

The paper studies fixed modes of linear time-invariant systems \(\dot x= Ax+ Bu\), \(y= Cx\), where \(x\in \mathbb{R}^ n\), \(u\in \mathbb{R}^ m\), \(y\in \mathbb{R}^ p\) and \(A\), \(B\), \(C\) matrices of appropriate size. An equivalent criterion for a simple eigenvalue of \(A\) to be a transmission zero or remnant zero is described. The result may be of use in large scale systems.