GA method for solving minimum rank problems in reduced-order H∞ synthesis

Reduced-order H_∞ synthesis can be referred to as a minimum rank problem under LMI constraints, which is a non-convex optimization problem. The paper presents a numerical method for solving the non-convex optimization problem using genetic algorithms, by which the minimum order k of the H_∞ controller and a corresponding parameter pair (X, Y) can be effectively found. The obtained results can be used to design an excellent reduced order H_∞ controller. Due to not depending on initial points, the proposed approach is characterized by global search. A numerical example illustrates the effectiveness of this method