On decentralized dynamic pole placement and feedback stabilization

In this paper we study the feedback control problem using an r-channel decentralized dynamic feedback control scheme. We will develop the theory in the behavioral framework. Using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded McMillan degree, and we show that this parameterization has the structure of an algebraic variety. We define the pole-placement map for this problem, and we give exact conditions when this map is onto, and almost onto. Finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set