Minimal symplectic orbits of rational contractive matrix functions

Abstract

The paper provides a state space characterization of the orbit of a rational matrix functionW(λ) which is a contraction on the real line and a strict contraction at infinity, under the set of all rational symplectic transformations acting minimally onW(λ). The principal tool is a geometric description of all minimal symplectic decompositions of such a function. A geometric description of all the minimal regular\(\left[ {\begin{array}{*{20}c} 0 & I \\ I & 0 \\ \end{array} } \right]\) decompositions of a selfadjoint on the line rational matrix function is also given.