GA-based H2/H∞ static output feedback design with average performance concept and techniques of family of polynomials

For continuous systems with polytopic uncertainties, the mixed H2/H∞ robust output control problem is considered in this paper. The design objective is to seek a static output feedback controller that is able to stabilize the uncertain system and to minimize the mixed H2/H∞ norm. To this end, a hybrid algorithm mixed by the technique of Hurwitz testing matrix of family of polynomial, average performance constraint and genetic algorithm (GA) is proposed. Due to the fact that the algorithm is based on GAs, we use a hierarchical structure to merge the conditions of Hurwitz testing matrix technique and average performance constraint into a fitness function which is called Hierarchical Fitness Function Structure (HFFS). By replacing fitness function with HFFS, any GAs can be applied to constitute the algorithm. Also, the proposed approach does not need any assumptions, so it is much more relaxed than that of Lyapunov-based design methods.