A state feedback controller was designed by Lyapunov stability theory,and the sufficient conditions were given to the implementation of synchronization of two delayed chaotic systems via linear matrix inequality technique.

By the approximation properties of fuzzy system and the Lyapunov stability theory, the parameter-adjusting laws are designed to guarantee that output of Smith-predictor can consistently converge to object output, and condition of convergence is deduced.

Based on Lyapunov stability theory, lag controller and update law of parameters are obtained.

The coupling functions of the connected nodes of the complex network are identified based on Lyapunov stability theory.

By employing the Lyapunov stability theory and linear matrix inequality(LMI)technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory(BAM)neural networks with time- varying delays.

The parameter self-adaptive rule designed by Lyapunov stability theory adjusts both fuzzy rule conclusion parameters and membership function pa.

Based on the Lyapunov stability theory,the designed controller is proved enable to globally stabilize asymptotically the controlled system to return to its zero balance point and minimize the proposed cost functional.

Special solutions of Kirchhoff equations and their Lyapunov stability;

Talking on the theory,methods and application of Lyapunov stability

The stability of the algorithm was analyzed, and the sufficient condition to make a closed-loop system stable was presented based on the Lyapunov stability theory.