Canonical Projector Techniques for Analyzing Descriptor Systems

Physical systems are often naturally formulated as descriptor systems (DSs) which form a superset of the more restrictive standard state spaces. The analysis of a DS, however, is complicated by the algebraic coupling between its proper and improper subsystems. The recently emerging canonical projector technique, stemming from iterative matrix chain construction, provides a theoretically sound and numerically effective way to completely decouple these subsystems and largely facilitates the reuse or adaptation of standard state space techniques for DS analysis. Nonetheless, results concerning canonical projectors are scattered and their potential use is currently less appreciated. The objectives of this paper are twofold: i) It serves as a tutorial that collects distributed results about canonical projectors and presents them in a coherent manner; and more than just a tutorial, it elaborates and provides new/elegant/corrected proofs to some fundamental properties of canonical projectors. An iterative procedure for canonical projector construction, lacking in the literature, is also described. ii) Obvious applications, including some latest development, of projector techniques in practical circuit design problems are succinctly illustrated. By creating a self-contained repository of important canonical projector theories, it is hoped that more interest will be drawn and efficient numerical implementations will follow.