Low-order H∞ controller design using LMI and genetic algorithm

This paper present a genetic algorithm optimization approach to treat with the low-order sub-optimal H_∞ controller design problems described by LMIs. The LMIs based low-order H_∞ controller design problems can be formulated as matrix rank minimization problem under LMIs constraint conditions. Due to matrix rank minimization problem is a non-convex NP-hardness problem, there are any feasible solutions by now. Facing to this problem, the paper presents a genetic algorithm strategy to deal with the multiobjective constraint optimization problem. By simultaneously optimizing the non-convex matrix rank minimization problem and H_∞ performance index, the feasible solution can be found for the desired low-order controller under different specification. This algorithm will benefit controller design when the controller software and hardware realization and specification will be satisfied simultaneously.