Design of H-infinity Robust Output Feedback Controller Using LMI Toolbox

This paper presents a methodology for designing H-infinity robust output feedback controllers utilizing MATLAB's Linear Matrix Inequality (LMI) Toolbox. The approach employs LMI-based optimization techniques to synthesize controllers with enhanced robustness, thereby improving system stability and performance metrics. The content begins with an explanation of fundamental H-infinity control theory concepts, including performance criteria and robustness requirements. It then details practical implementation using MATLAB's LMI Toolbox, covering key functions such as lmivar() for defining matrix variables, lmiterm() for constructing LMI conditions, and mincx() for solving convex optimization problems. Specific design steps include: 1. Formulating the H-infinity control problem as LMI constraints 2. Implementing the output feedback structure using matrix variable definitions 3. Solving the LMI system with feasibility checks 4. Extracting controller parameters from solution matrices The implementation process demonstrates how to code the LMI conditions for H-infinity performance specifications, with emphasis on handling multi-objective constraints. Simulation results validate the method's effectiveness through comparative analysis of robustness indicators and performance metrics. The discussion further explores practical application scenarios and potential advancements in robust control system design.