One input control of exponential synchronization for a four-dimensional chaotic system

The purpose of this paper is to concern the exponential synchronization of the four-dimensional (4D) Lorenz–Stenflo chaotic system by utilizing one input linear feedback control. There are two main results provided. Firstly, for two identical chaotic systems, two types of one input controllers with single state linear feedback applied to the slave system are introduced. Then, these one input linear feedback controllers associated with the corresponding system parameter updated rules are also developed for two non-identical chaotic systems. Sufficient conditions are proven based on the exponential stability and numerical simulations are proposed to demonstrate the effectiveness of the present schemes.