中文摘要：

研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性.

英文摘要：

A lot of studies of control highlight fractional calculus in modeling systems and designing controllers have been carried out. More recently, a lot of chaotic behaviors have been found in fractional-order systems. Then, controlling the fractional-order systems, especially controlling nonlinear fractional-order systems has become a hot research subject. The design of state estimators is one of the essential points in control theory. Time delays are often considered as the sources of complex behaviors in dynamical systems. A lot progress has been made in the research of time delay systems with real variables. In recent years, fractional-order time-delay chaotic synchronization and chaotic secure communication have received ever-increasing attention. In this paper we focus our study on the synchronization of fractional-order time-delay chaotic systems and its application in secure communication. Firstly, based on the Lipschitz condition, the nonlinear fractional-order time-delay system is proposed. Secondly, the fractional-order time-delay observer for the system is constructed. The necessary and sufficient conditions for the existence of the fractional-order observer are given by some lemmas. Thirdly, the synchronous controller is designed based on the state observer and the stability theory of fractional-order system. Instead of the state variables, the output variables of drive system and response system are used to design the synchronous controller, which makes the design much more simple and practical. With the Lyapunov stability theory and fractional order matrix inequalities, the method of how to obtain the parameters of the controller is presented. The sufficient conditions for asymptotical stability of the state error dynamical system are derived. After that,with the Chen fractional-order time-delay chaotic system, the synchronous controller is designed to make the system run synchronously. Finally, the proposed approach is then applied to secure communications, where the information signal is injected into