Design of Reduced-Order, H2 Optimal Controllers Using a Homotopy Algorithm

The minimal dimension of a linear-quadratic-gaussian (LQG) compensator is usually equal to the dimension of the design plant. This deficiency can lead to implementation problems when considering control-design for high-order systems such as flexible structures and has led to the development of methodologies for the design of optimal (or near optimal) controllers whose dimension is less than that of the design plant. This paper develops a new homotopy algorithm for the design of reduced-order, H2 optimal controllers. The algorithm has been implemented in MATLAB and the results are illustrated using a benchmark, non-colocated flexible structure control problem.