Judgement on the existence of a common quadratic Lyapunov function for a kind of systems;

This paper uses a piecewise linear Lyapunov function and derives a new estimate for solutions of linear time-varying systems.

After Lyapunov function is de- rived,with theoretical analysis,energy-based control design method is discussed in order to solve the global stability problem.

Based on the common disturbed motion equation of projectiles, Liapunov functionV(X)=XH eX in plural number mode is constituted with the help of Hermite matrix H e and Liapunov s direct method.

Furthermore,according to the method of Liapunov functions in the stability theory,both the globally asymptotic stability and the attractive regions of the nonnegative equilibrium in the model are discussed.

It is discussed that the methods of discrimination of the stability of the singular point of nonlinear autonomous system by using of eigenvalue,center manifold and Liapunov function.

In order to study the stability of longitudinal following control system of vehicle in automated highway system,the following errors of vehicles were analyzed,a mathematic model of infinite-dimensional nonlinear interconnected large-scale system with delays was constructed,and the stability of the system was studied by applying vector Liapunov function.

Based on the theory of topology and the properties of M-matrix, by constructing vector Liapunov function and applying differential inequalities, the exponential stability of three classes of interconnected large-scale systems with time delays is analyzed.