An LMI Approach to Robust $H_{\infty}$ Guarantee Cost Control for LLCL-filtered Inverters Connected to a Weak Grid

This paper adopts a polytopic model to describe a parametric uncertain system and then proposes a direct grid current robust H∞ guarantee cost controller based on linear matrix inequalities (LMIs) for the three-phase LLCL-filtered grid-connected inverters. The H∞ controller is designed to assure robust stability and an upper bound on H∞ performance of the closed-loop system under grid impedance uncertainty and grid voltage distortion conditions. The simulation and experimental results compared with other two robust controllers with a 9.1-kW three-phase LLCL-filtered grid-connected inverter validate the feasibility and superiority of the proposed method.