H∞ state feedback controller design with mixed frequency specifications

This paper is concerned with the H_infin control problem for linear continuous-time systems in mixed frequencies ranges. A state feedback controller is designed such that the resulting closed-loop system is asymptotically stable and satisfies entire frequency and finite frequency H_infin performance respectively. Then a sufficient condition for the existence of the controller is derived in terms of linear matrix inequalities (LMIs). Compared with the existing result, our design procedure reduces the conservatism and improves the performance in the multi-objective setting. Finally a numerical example is given to illustrate the effect of the proposed method.