Controllability, observability, and duality in singular systems

Abstract

The concepts of controllability and observability for systems of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E\dot{x} = Ax + Bu, y = Cx, E</tex> singular are considered. A theory is presented which unifies the three main approaches to this topic already existing in the literature. The development includes a generalization of the duality theorem from state-space theory.