Static Output Feedback LMI for Discrete-Time Multivariate PID Controller Synthesis

The static output feedback controller design is one of the most important problems in control theory. The problem consists of finding a time-invariant output feedback gain that achieves closed-loop stability. This paper has two main contributions. First, a new condition for the static output feedback stabilization problem of linear discrete-time systems with direct-feedthrough terms is presented. Second, a new synthesis method for multivariate PID controllers is developed. The effectiveness of the proposed method is demonstrated by several numerical examples.