Optimization of coordinate transformation matrix for discrete-time H∞ static-output-feedback control problems

The problem of how to select a coordinate transformation matrix to improve the LMI conditions for H
_∞
static-output-feedback (SOF) control of discrete-time systems is a challenging open problem. This paper applies a newly proposed strategy to solve this problem. An iterative algorithm is developed to produce controllers with locally optimal closed-loop H
_∞
performances. The algorithm is also applied to other H
_∞
SOF control problems, such as decentralized H
_∞
SOF control and simultaneous H
_∞
SOF control. Finally, numerical examples are provided to demonstrate the effectiveness and advantages of the proposed method.