On Design of H∞ Structured Controller for Decentralized Control systems

In this paper the problem of $H_{\infty}$ structured controller design is addressed. The considered problem arises when selection of actuators in decentralized control systems leads to that some rows of the controller gain matrix should be zero. However, the design of controllers with sparse structure is essentially a combinatorial problem that is hard to handle. Towards this end, this paper adopts a mixed-integer programming method to tackle the resulting row-cardinality constraint. The direct mixed-integer programming method is utilized to assist in designing row-sparse $H_{\infty}$ state feedback controllers for large-scale distributed systems.