中文摘要：

为了研究一个三维自治混沌系统的控制与同步问题，应用自适应控制方法研究混沌系统不稳定平衡点的镇定问题，得出了该系统关于平衡点渐近稳定的一个充分条件，并利用Lyapunov函数和LaSalle不变原理对结论给予了严格的证明。设计了一个较简单的控制器，采用非线性反馈控制方法研究了此混沌系统的错位同步问题，实现了响应系统和驱动系统之间的错位同步，并在Matlab上进行实例仿真。仿真结果表明自适应控制方法的快速有效性和错位同步的可实现性。

英文摘要：

This paper deals with the control and synchronization of a new three-dimensional continuous quadratic autonomous chaotic system. First, by utilizing adaptive control approaches, the stabilization of unstable equilibrium points of the chaotic system was studied; a sufficient condition of the asymptotical stableilization of equilibrium points was given; the strict proofs were presented in terms of Lyapunov functions and LaSalle invariant principle ; then a simple controller was designed; the mismatch synchronization of this chaotic system was investigated by nonlinear feedback control method, and the mismatch synchronization between drive system and respond system was achieved. Several numerical simulations by Matlab were given to show the effectiveness of the proposed chaos adaptive control and mismatch synchronization methods.