Robust Control MATLAB Example: H-infinity and H2 Control Implementations

This document provides practical MATLAB implementations of robust control methodologies, featuring working code examples for H-infinity optimal control, H-infinity control, and H2 control techniques. The implementations were developed following established textbook examples to ensure academic rigor and practical applicability. The H-infinity optimal control methodology focuses on designing controllers that maintain system performance despite model uncertainties and operational disturbances. The implementation typically involves solving Riccati equations using MATLAB's `hinfsyn` function, which calculates optimal controllers that minimize the worst-case gain from disturbances to outputs. H-infinity control represents a broader approach applicable to various control scenarios, implemented through MATLAB's robust control toolbox functions like `hinf` and `mixsyn`. These functions enable controller synthesis that addresses multiple performance specifications simultaneously while maintaining robustness. H2 control techniques specialize in minimizing the impact of external disturbances on system performance. The MATLAB implementation commonly utilizes the `h2syn` function, which designs controllers to minimize the H2-norm of the closed-loop transfer function from disturbances to outputs, making it particularly effective for systems where stochastic disturbances significantly affect performance. All code examples include practical implementation details such as system modeling using `ss` (state-space) objects, weight function selection for performance shaping, and controller synthesis procedures with proper validation checks using functions like `sigma` for frequency response analysis.