Controllers designed by u-synthesis for the next generation air-to-air missile are constraint by the ability of the current CPU. So that these controllers have many problems, i.e. high order stiff and moreover bad condition, a new arithmetic called ‘Implicit Euler and Extrapolate’ is put forward. Through comparison of declination bound estimation and close-loop robustness after reduction are analyzed between these two reduction means, which validates that Hankel norm approximation performs better reduction effect as well as better performance holding. Due to stiff feature, a new arithmetic called ‘Implicit Euler and Extrapolate’ for implementing the μ-synthesis controller is introduced which also show better astringency than other arithmetic. At the same time, the running rate reach 2ms per step only, satisfying the real-time requirement.