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

In this note, sufficient conditions for H_∞ output feedback stabilization of linear discrete-time systems are proposed via linear matrix inequalities (LMIs). In order to reduce conservatism existing in earlier LMI methods, auxiliary slack variables with structure are employed. It is shown that degree of freedoms by the introduction of auxiliary slack variables lead to more flexibility in obtaining an approximate solution of H_∞ output feedback stabilization problems. Consequently, the proposed method can yield a less conservative result than 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.