GA-based robust S-stability output feedback controller design algorithm with hierarchical fitness function structure

In this paper, the output feedback controller design problem with robust S-stability constraint is considered. The S-stability constraint denotes that the controller can stabilize the uncertain system and shift all closed-loop poles of nominal system inside a specific conic sector s. We intend to simple genetic algorithm (SGA) to seek these robust output feedback gains. To this end, we develop the hierarchical fitness function structure (HFFS) to combine the stability conditions so that the fitness value corresponds to the stable degree of closed-loop system. These stability conditions of HFFS are derived by means of the concept of family of polynomials, generalized edge theorem and Hurwitz testing matrix. The proposed design algorithm is named the robust S stability output feedback controller design algorithm (RSOFCDA).