Missile stability control system is one of the crucial technologies to promote missile guidance performances， and has always been a research hotspot and focus. Taking the longitudinal plane of a missile as an example， a state-space model of the missile stability control is established. The linear quadratic regulator （LQR） control algorithm is derived， and an improved PID（proportional integral derivative）-LQR approach for missile stability control is proposed based on the traditional LQR method and PID algorithm. The control performances of the proposed method are compared with traditional LQR method， improved LQR method， and fuzzy PIQ-LQR method through simulation analysis. The established missile model parameters are subjected to conduct bias tests. The simulation results show that the proposed method is superior to the other three methods and has good control performances and robustness.

The notch filter is usually used to suppress the elastic vibration frequency of the missile body when the missile stability control is designed， so as to ensure the elastic stability of the missile body in the control system. The basic principle of the notch filter was introduced， and an improved pre-distortion bilinear transformation approach was proposed to address the frequency distortion problem caused by the discretization design of the notch filter. Compensation for the frequency distortion was achieved by adjusting the damping magnitude without changing the damping ratio of the notch filter. Compared with the traditional discretization method， the proposed method not only compensates for distortion frequency but also ensures that the notch width and phase characteristics are the same as those in the continuous domain， and the proposed method has the advantages of simple operation and strong adaptability.

In order to achieve the intercept mission requirements， an improved optimal guidance law is derived considering the angle constraint of the interceptor and the premature loss of energy that cannot satisfy the subsequent interception requirements. Based on the structure of energy minimum objective function， a control weighted function is proposed to minimize the required overload in the initial phase and the terminal line of sight （LOS） angle can converge to the excepted value. An angle constraint optimal guidance law is derived in view of small angle assumption and optimal control theory. Based on the characteristics that the guidance law can make the terminal LOS angle converge， the problem of terminal LOS angle is converted into the problem of terminal encounter angle， and the optimal guidance law with terminal-intersection angle constraint is obtained. The simulation results show that the designed guidance law can not only realize terminal encounter angle control， and also ensure low energy consumption in the initial stage of guidance， as well as achieve high hit accuracy. The designed approach has certain reference and application values for the study on the optimal guidance law of interception missile.