On Synthesizing Partially Decentralized Controllers

Quite often, in the control of physical systems, structural constraints are placed on the feedback controller. Issues of complexity, computation, ease of implementation and physical dimensions play a role in the decision to select structurally constrained controllers. This paper examines controllers which are constrained by the amount of information sharing occurring in the feedback channels. A fully decentralized controller is characterized by no sharing of information among the feedback channels. Three other types of partially decentralized controllers are characterized by the way in which the feedback channels locally share information between adjacent channels. It is shown in this paper via left and right unimodular transformations, that from the set of stabilizing decentralized controllers associated with a transformed plant operator a set of stabilizing partially decentralized controllers can be recovered. This serves to identify a potentially useful methodology for the synthesis of partially decentralized controllers by formulating the problem within a framework which can take advantage of the stable factors approach to the parameterization of the set of all stabilizing fully decentralized controllers.