H-infinity Control System

H-infinity control is a robust control methodology designed to maintain system stability and performance under uncertainties and external disturbances. This approach optimizes the H-infinity norm of the controller's transfer function (representing the peak gain in frequency response) to suppress worst-case disturbances effectively.

In MATLAB, H-infinity control system design typically involves the following implementation steps: System Modeling: Represent the plant using state-space or transfer function formulations. Weighting Function Selection: Define appropriate performance weighting functions (such as sensitivity and complementary sensitivity functions) to balance robustness and performance requirements. Controller Synthesis: Utilize functions like `hinfsyn` to compute the optimal H-infinity controller. This function employs gamma-iteration algorithms to identify controllers meeting design specifications through iterative optimization. Validation and Analysis: Evaluate controller robustness and performance through frequency-domain analysis (e.g., Bode plots) or time-domain simulations (e.g., step response tests).

H-infinity control is particularly crucial in aerospace, autonomous driving, and other high-stakes applications due to its capability to handle model uncertainties and high-frequency noise effectively. MATLAB's Control System Toolbox provides a comprehensive toolchain that streamlines the entire workflow from modeling to verification, featuring specialized functions for robust control analysis and synthesis.