The procedure of applying the theory of similarity to LQR method in aeroengine control systems was developed.The method was analyzed and the shortcomings were pointed out:(1) the closed-loop system responds slowly at high altitude and low Mach number

which can not meet the swift respond requirement;(2) the closed-loop system requires too much control energy at low altitude and high Mach number.On one hand

this is very likely to cause aeroengine actuator saturation.On the other hand

this would degrade the performance of the closed-loop system under disturbances such as noises and delays.Hence

an improved procedure of applying the theory of similarity was developed and it solved the above problems reasonably well.Further more

the stability of the proposed method was proved.It was also extended to the augmented LQR method.Finally

the design procedure of a turbofan engine control system exemplified the above results.