By means of Lyapunov stability theorem,it is proved that the dynamics of the synchronization error is globally and asymptotically stable.

Considering the varying of velocity of the missile and target, the classical differential geometry curve theory approach and Lyapunov stability theory are combined to create a new design approach to three dimensional missile guidance problems.

A three-dimensional guidance law was designed by using Lyapunov stability theory,which was based on the dynamics and kinematics of the relative motion between missile and target for missile guidance,and under the assumptions that the target was stationary,and the velocity of missile was a constant.

A new robust dynamic inversion controller design is introduced for air-to-air missiles by combining (dynamic) inversion and robust control based on Lyapunov stability.

According to the dynamic equation of relative motion between the missile and the target,Lyapunov stability theory is used to design a new yaw plane guidance law for missiles.

In Ibis paper,a novel control law for achieving output regulation was derived directly from applying Lyapunov stability theory based on Boost bilinear system model.

The control law is derived from directly applying the Lyapunov stability theory to the bilinear large signal models, so that the closed loop systems possess excellent output characteristics.

Our theoretical analysis is as usual based on Lyapunov stability theory and inverse dynamic method.

Using the concept of the second method of Liapunov stability theory,a Liapunovfunction δ￣2S related to the differential equations of atmospheric disturbance is obtained.