一类由耦合Lorenz系统组成的大系统的同步与镇定

研究了由N个结构相同的耦合Lorenz系统组成的大系统的同步和镇定问题,且这类大系统是通过各子系统的第一个状态变量耦合的.当系统未加控制的时候,通过选择一个自适应率,给出了使大系统同步的充分条件;如果选择合适的控制器,大系统能够被镇定.这个控制器由两部分组成,一部分是状态反馈控制器,状态反馈控制的优点是结构简单,易于实现;另一部分是和耦合系数相关的控制量,且充分条件是由线性矩阵不等式(LMIs)表示.最后,仿真例子证明了提出方法的可行性和有效性.

Synchronization and Stabilization of a Large-Scale System Composed of Coupled Lorenz Systems

The synchronization and stabilization issues are investigated for a large-scale system,which is composed of N identical Lorenz systems and they are coupled together with the first state variable of each subsystem.When uncontrolled,the sufficient condition of synchronization for such the large-scale system is derived by choosing an adaptive feedback gain equation.And if choosing an appropriate controller,the large-scale system can be stabilized.Such a controller is composed of two components,i.e.,the state feedback controller is simple and easy to implement,and the other one relates to coupling coefficient.As a result,the final expression is in the terms of the Linear Matrix Inequalities(LMIs).A simulation example is provided to illustrate the design procedure of the proposed method and its feasibility and effectiveness.