INVARIANT SUBSPACES AND INVERTIBILITY PROPERTIES FOR SINGULAR SYSTEMS - THE GENERAL-CASE

Open-loop definitions and properties of several subspaces for general singular systems are characterized by means of a fully algebraic distributional framework. Simple recursive algorithms for producing these spaces as well as related duality aspects tum out to follow directly from these definitions. Next, we provide definitions and conditions for two notions of left (light) invertibility of a general singular system in terms of our distributions, subspaces, and Rosenbrock's system matrix, and we show which conditions represent the ''gap'' between our invertibility concepts. Finally, we prove that in many cases left (right) invertibility is equivalent to left (right) invertibility of the system matrix.