What is H-infinity control and when is it used?

H-infinity control designs controllers minimizing the H-infinity norm (maximum gain over frequency) of a closed-loop transfer function, typically from disturbance to error. This provides guaranteed worst-case performance bounds despite model uncertainty. Design specifies weighting functions shaping sensitivity at different frequencies. Robust stability is achieved by keeping complementary sensitivity bounded. H-infinity outperforms classical methods when model uncertainty is significant. Solved using Riccati equations or LMI optimization. Common in aerospace, where uncertainty bounds must be guaranteed.