H infinity

H_∞ or H infinity is a method in control theory for the design of optimal controllers. Essentially it is an optimization method, that takes into consideration astrong mathematical definition of the restrictions on the expected behaviour of the closed loop and the strict stability of it. It noted for its strong mathematical foundation, the mathematical way to express engineering restrictions, its optimization/optimality aspect and the ability to include both classic and robust control concepts within a single design framework.

The "H" stands for Hardy space. "Infinity" implies that it is designed to accomplish minimax restrictions in the frequency domain. The H_∞ norm of a dynamic system is the maximum amplification the system can make to the energy of the input signal. It is equal to the system's maximum singular value, the maximum value of its frequency response magnitude.