Unified canonical forms for linear time-varying dynamical systems under D-similarity transformations. II

Abstract

For pt.I see ibid., p.74-81. The linear differential equation operators, D spaces, and D-similarity transformations introduced in pt.I, are used to establish a number of results for the analysis of time-varying linear dynamical systems. In particular, the concepts of D-characteristic equations (which include the well-known Riccati equation as a special case), essential D (ED) eigenvalues, ED eigenvectors, and ED eigenspaces for vector and scalar time-varying linear systems are presented. Two spectral canonical forms for time-varying linear systems and four canonical D-similarity transformations that relate the classical companion canonical forms with the time-varying spectral canonical forms are developed. These canonical forms serve to unify the classical Jordan and diagonal canonical forms and the classical (generalized) Vandermonde matrix for the general class of time-varying linear systems. >