The decentralized implementability problem

This paper deals with the problems of decentralized implementability and decentralized regular implementability in the context of finite-dimensional linear differential system behaviors. Given a plant behavior with a pre-specified partition of the system variable and a desired behavior, the problem of decentralized implementability is to find a controller which is decentralized with respect to the given partition and implements (regularly) the desired behavior with respect to the plant. In this paper we formulate these problems in the behavioral framework, with control as interconnection and we also provide necessary and sufficient conditions for the solvability of these problems.