Poles and zeros at infinity of linear time-varying systems

The notions of poles and zeros at infinity and their relations are extended to the case of linear continuous time-varying systems. This study is based on the notion of a “newborn system” which is, in a mathematical point of view, a graded module extension over the noncommutative ring of differential operators. It is proved to be a relevant generalization to the time-varying case of the equivalence class, for the so-called “restricted equivalence” of Rosenbrock’s polynomial matrix descriptions. The authors’ approach is intrinsic and unifies the definitions previously given in the literature in the time-invariant case.