Sufficient LMI conditions for the H∞ output feedback stabilization of linear discrete-time systems

In this note, sufficient LMI conditions for the H_∞ output feedback control design of linear discrete-time systems are proposed. In order to reduce conservatism existing in earlier sufficient LMI methods, auxiliary slack variables with structure are employed. It is shown that the slack variables employed in this note provide additional flexibility in solving the H_∞ output feedback control problem. Consequently, the proposed method can yield a less conservative result than that of earlier LMI methods. In particular, typical output feedback control problems, such as decentralized H_∞ output feedback control and simultaneous H_∞ output feedback control, can be more efficiently solved. Numerical examples are included to illustrate the advantages of the proposed LMI method.