Robust static output-feedback control for uncertain linear discrete-time systems via the generalized KYP Lemma

This paper is concerned with robust static output-feedback (SOF) control for linear discrete-time systems subject to polytopic uncertainty and restricted frequency-domain specifications (RFDSs) via the generalized Kalman-Yakubovich-Popov (KYP) lemma. Polytopic uncertainties are assumed to enter all the system matrices, while RFDSs are motivated by the fact that practical design specifications are often described in restricted finite frequency ranges. Dilated multipliers are first introduced to relax the GKYP lemma for SOF controller synthesis and robust performance analysis. Then a two-stage approach to SOF controller synthesis is proposed: at the first stage, a robust full-information (FI) controller is designed, which is used to construct a required SOF controller at the second stage. To improve the solvability of the synthesis method, an iterative algorithm is further formulated for exploring the SOF gain. The effectiveness of the proposed design method is finally demonstrated by a numerical example.