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.