On Power Balancing and Stabilization for a Class of infinite-dimensional systems

In this paper we present control of infinite-dimensional systems by power shaping methods, which have been used extensively for control of finite dimensional systems. Towards achieving the results we work within the Brayton Moser framework, by using the system of transmission line as an example and derive passivity of the system with respect to the boundary voltages and derivatives of current at the boundary. We then solve the stabilization problem by interconnecting the system through a finite-dimensional controller and generating Casimirs for the closed-loop system. Finally we explore possibility of generating other alternate passive maps.