Finite Dimensional Controller Design for Infinite Dimensional Systems: A Passivity Approach

A new control design method for distributed parameter systems is introduced in this paper. The key idea is to use the passivity theorem to analyze closed loop stability instead of the commonly used small gain theorem. An algorithm is presented for designing stabilizing finite dimensional controller for unstable infinite dimensional systems with bounded input and output operators. This class of controller is typically of equal or smaller order than those obtained based on the small gain method.