H-infinity control in a behavioral context: The full information case

In this paper the authors formulate the H-infinity-control problem in a beh avioral setting. Given a mathematical model, say a set of higher order diff erential equations together with some static equations, the vector of manif est variables (i.e., the variables to be modeled) is partitioned into yet t o be controlled variables, unknown exogenous variables (called disturbances ), and interconnection variables. The interconnection variables are availab le for interconnection, in the sense that they can be made to obey certain differential or static equations, to be specified by the designer. Such a s ystem of differential equations and static equations is called a controller . The design problem that we consider is to find controllers such that (in the L-2-sense) the size of the to be controlled variables is less than a gi ven tolerance, for all disturbances in the unit ball, and such that the int erconnection is a stable system. We find necessary and sufficient condition s for the existence of suitable controllers, under the hypothesis that we h ave a full information problem, These conditions involve indefinite factori zations of polynomial matrices and a test on a given Pick matrix.