Fixed order controller design via generalized KYP lemma

This paper proposes methods for fixed-order controller synthesis based on the generalized KYP (GKYP) lemma that provides a unified LMI characterization of frequency domain inequalities in (semi) finite frequency ranges for both continuous and discrete-time systems. We first show the GKYP lemma and how to use it for control system design including PID controller synthesis and controller order reduction with fixed poles. We then propose a recursive algorithm for fixed structure controller synthesis, where both the numerator and denominator are design parameters. We also provide a robust GKYP lemma to encompass the practical situations. The effectiveness of the proposed methods is verified by several numerical examples which include a practical application of tracking controller design for laser-driven micro-airplanes.