One input control for exponential synchronization in generalized Lorenz systems with uncertain parameters

By taking account of uncertain slave system parameters, the main goal of this paper is to investigate exponential master-slave synchronization between two nearly identical generalized Lorenz systems via one control input, which including a single state proportional feedback, associated with system parameter estimated laws, which not including states of the master system. Sufficient conditions are provided for the guaranteed exponential stability of both synchronized errors and system parameter errors. Meanwhile, numerical studies are also performed to verify the effectiveness of presented schemes.