H∞ control in a behavioral context

Recently, it has been argued that in many cases it is more natural to view the problem of controller design as the problem of designing for a given system an additional set of `laws´ that the the signals appearing in the system should obey. More specifically, if a system is given in terms of a certain set of `behavioral equations´, then the problem of controller design is to invent an additional set of equations, involving the signals appearing in the system, in such a way that the `controlled system´ satisfies the a priori given control specifications. In this paper, we attempt to reformulate and study the H _∞ control problem in the behavioral framework, i.e., in the framework one gets by taking the alternative point of view to controller design