In the paper,using the method of the Liapunov transformation and making a study of the Riccati equation,we give some results to determine the sign of characteristic exponent of two-dimensional periodic linear systems.

via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues.

Midcourse guidance based on Lyapunov optimal feedback control;

Based on the six degree of freedom (DOF) nonlinear dynamic model of airship, the stability and controllability of airship are analyzed by using the first approximate theory of Lyapunov and the method of approximate linearization respectively.

The methods based on Linear Quadratic Regulators(LQR)theory,Lyapunov stability theory and Zero Effort Miss method are used to design controllers respectively.

In this paper, the authors study an SIS epidemic model with a finite distributed time delay, by means of Liapunov functional, some sufficient conditions of global stability to endemic equilibrium and disease free equilibrium have been obtained.

According to the catastrophe of instability of slope,the strange point catastrophe model of the slope system is set up by using the chaotic theory and it is forecast whether the system is chaos by using some methods such as pointcare reflection method,lyapunov exponent method and fractal dimension method,etc.

And it explains the application of Lyapunov exponent in the chaos of the electrical engineering.

Then Poincare diagrams on different sections,Lyapunov exponents diagrams and bifurcation diagram from the period-doubling regime to chaotic counterpart were provided.