Factorization of linear systems: a generalized framework

AbstractA generalized module theoretic framework for the study of linear time invariant systems is developed. Crucial in the present discussion are two new notions: the generalized “order” and the “adapted bases”. These notions form generalizations of the classical concepts of order (or degree) and of proper bases, employed in the theory of linear systems. The resulting framework is then applied to obtain explicit conditions for system factorization, and to study output feedback systems in which the feedback compensator is stable