Controller synthesis for multiple finite frequency specifications: Dissipation inequalities approach

Many of practical design specifications are provided by finite frequency properties described by inequalities over restricted finite frequency intervals. The properties are known as the important property in integrated design and robust control. Recently, the authors proved that the property is equivalent to some dissipation inequality using quadratic differential forms which is a useful algebraic tool in the dissipation theory based on the behavioral approach. In this paper, we consider a synthesis of a controller for finite frequency properties and derive a necessary and sufficient condition for the achievability of a controller satisfying with multiple finite frequency specifications in terms of dissipation inequalities as a main result. This result clarifies a physical interpretation of the controller from the viewpoint of dissipation theory. We also derive a method for computing a polynomial matrix which induces the controller based on the result.