The Behavioral LQ-problem for linear nD systems

This paper deals with systems described by constant coefficient linear partial differential equations (n-D Systems) from a behavioral point of view. The performance functional is the integral of a quadratic differential form. In this case an appropriate tool to express quadratic functionals are 2-n variable polynomial matrices. We look for a characterization of the set of stationary trajectories and for the set of local minimal trajectories with respect to compact support variations, turning out that they are equal if the system is dissipative. Finally we implement these trajectories of the given plant as a (regular) interconnection of the plant and a controller.