Invariants and Canonical Forms under Dynamic Compensation

This paper is concerned with the development of a complete abstract invariant as well as a set of canonical forms under dynamic compensation for linear systems characterized by proper, rational transfer matrices. More specifically, it is shown that one can always associate with any proper rational transfer matrix, $T(s)$, a special lower left triangular matrix, $\xi _T (s)$, called the interactor. This matrix is then shown to represent an abstract invariant under dynamic compensation which, together with the rank of $T(s)$, represents a complete abstract invariant. A set of canonical forms under dynamic compensation is also developed along with appropriate dynamic compensation.