A Further Study on Output Feedback $\mathcal{H}_{\infty}$ Control for Discrete-Time Systems

This brief further studies the problem of output feedback H
_∞
control for discrete-time systems. A new condition for output feedback H
_∞
controller design is proposed. The condition is represented in the form of linear matrix inequality (LMI) with two scalar parameters. In comparison with the existing results, the proposed condition decreases the dimension of the matrix inequality. A rigorous theoretical proof is given to show that the proposed design condition is less conservative than some existing conditions. The effectiveness of the proposed condition is successfully demonstrated by a numerical example.