中文摘要：

本文针对异构不同维的混沌系统主从同步问题进行了研究.基于事件触发的采样控制器被设计用来实现主从混沌系统的同步.首先针对系统中所包含的传输时滞,构造系统时滞模型.基于所设计的时滞模型,采用输入延迟的方法将同步控制器求解问题转化为所对应时滞系统的稳定性问题.然后通过构造Lyapunov-Krasovskii泛函并结合Wirtinger不等式和自由权矩阵,给出了异构混沌系统同步的条件和采样控制器的求解方法.所设计的采样控制器只有在触发规则满足的条件下,才更新控制参数,降低了网络的使用率.最后通过数值仿真验证了所提出方法的有效性.

英文摘要：

As is well known, chaos synchronization has a good performance in secret communication. However, in most existing researches, chaos synchronization is realized between master chaotic system and slave chaotic system with real-time communication. A lot of network bandwidths are wasted in useless communication which may bring great economic costs and increase the likelihood of network congestion. In this paper, the synchronization for the heterogeneous master-slave system is studied. Compared with the homogeneous synchronization, the heterogeneous synchronization has a broad application prospect. Then the sampling controller based on event trigger is designed to achieve the heterogeneous master-slave synchronization which can save network bandwidth, with the control performance maintained.Because transmission time delay is universal in communication system, the delay model of the system is constructed and utilized firstly. Based on the proposed system model, the master-slave heterogeneous synchronization problem is equivalently converted into the asymptotical stability problem of a time-delay system by using the input delayed approach. Then, according to the Lyapunov stability theory and linear matrix inequality, we may rigouously prove that the synchronization of heteogeneous master-slave chaotic system can be achieved. Meanwhile, the heterogeneous master-slave system synchronization conditions and sampling controller can be given based on the constructing LyapunovKrasovskii functional with the Wirtinger inequality and free weight matrix method. The sampling controller actually is a stateback controller. But for the purpose of reducing the network usage rate, wheter the state can be transmitted can be determined by the event-triggered rules. The event-triggered rules are designed based on the error state between master chaotic system and slave chaotic system, and the synchronization performance index can be determined by choosing the system parameter. The designed sampling controller updates the control parameters