Exponent stability of the system was presented using 2nd Lyapunov method and linear matrix inequalities(LMI) formulation,and the state-feedback control parameters of DCS could be obtained according to the stability criterion.

By using the second method of Lyapunov,self adapting identification restrains of rotor speed and stator resistance were proposed.

Motion planning of non-holonomic mobile manipulator based on Lyapunov method;

Asymptotic stability analysis and stabilization for generalized systems via Lyapunov methods;

Based on Lyapunov methods, the hierarchical motion planning of free-flying dual-arm space robots for obstacle avoidance is discussed.

With the assumption that the variable parameters are unavailable,a parameter estimate rule and an adaptive learning control law for autonomous rendezvous in the elliptical orbit are designed via Lyapunov methods.

A nonlinear feedback controller, which can globally asymptotically stabilize the closed-loop system, was proposed based on the Lyapunov approach.

Although Lipschitz constants of function matrices and bounds of uncertainties were unknown,the Lyapunov approached guarantees the error system stab.

The Lyapunov approach was utilized to stabilize the observer error dynamics, and new stable conditions were constructed.