Gear-shift process of automatic transmission (AT) can be achieved with hydraulic control system which operates clutches or brakes' engagement or disengagement. According to the state of engagement elements, gear-shift process can be divided into torque phase and inertia phase. This article analyses gear-shift process of automatic transmission with the lever analogy and got the variation of the transmission's output torque. Then, the control principle of clutch to clutch shift is studied.This article takes power on up shift as study example and minimum of transmission output torque fluctuations during shifting as control target. Then this article analysis two control principles including inertia phase engine & transmission integrated control principle and entire shift process engine & transmission integrated control principle. For the factors that affect shifting during different stages and the characteristics of different shift control principles, clutch pressure observer based on input-to-state stability (ISS) is designed and applied to the entire shift process engine & transmission integrated control principle. Finally, the proposed control principle is applied on the vehicle simulation platform, Simulation results are compared to the results of power-on up shift without engine & transmission integrated control and integrated control strategy based on the transmission output torque observer which is designed based on the torque converter model. It is proved that the transmission output torque overshoot peak with inertia phase engine & transmission integrated control strategy is decreased significantly and shifting jerks are reduced. Shift quality is improved significantly.