Characterizing all classes of LTI stabilizing structurally constrained controllers by means of combinatorics

The focus of this paper is directed towards the problem of characterizing the information flow structures of all classes of LTI structurally constrained controllers with respect to which a given interconnected system has no fixed modes. Any class of structurally constrained controllers can be described by a set of communication links, which delineates how the local controllers of any controller in that class interact with each other. To achieve the objective, a cost is first attributed for establishing any communication link in the control structure. These costs are part of design specifications and represent the expenditure of data transmission between different subsystems. A simple graph-theoretic method is then proposed to characterize all the relevant classes of controllers systematically. As a by-product of this approach, all classes of LTI stabilizing structurally constrained controllers with the minimum implementation cost are attained using a novel algorithm. The primary advantages of this approach are its simplicity and computational efficiency. The efficacy and importance of this work are thoroughly illustrated in a numerical example. This paper integrates the ideas proposed in a recently published work and some original techniques to develop its main results.