一类扩展结构大系统分散关联镇定的LMI方法

研究一类扩展结构大系统的分散关联镇定问题.假设大系统是在原系统结构上一个个地增加新的子系统而构成,即所谓扩展结构系统,则扩展结构系统的分散镇定问题就是在不改变原结构分散控制律的基础上设计新加入子系统的分散控制律,使加入新子系统后的整个大系统仍能保持稳定且关联稳定.基于Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,推导了一类扩展结构大系统分散关联镇定的充分条件,并给出扩展结构的分散镇定控制器的设计方法.通过算例说明了所提出方法的有效性.

LMI Approach of Decentralized Connective Stabilization for Expanded Structure of Large-Scale Systems

The decentralized connective stabilization problem of the expanded structure of large-scale systems is considered. It is assumed that a large-scale system is constituted by adding new subsystems iteratively on the original one, i. e., an expanded system. Then, the decentralized connective stabilization problem of the system becomes how to design the local control law of the new subsystems without changing the decentralized control laws of original structure. Therefore, the subsystems and, as a result, the expanded system are both stable and connectively stable. The sufficient condition for the decentralized connective stabilization of the expanded structure of large-scale systems is obtained by use of Lyapunov theory and LMI approach. The design method of the decentralized stabilization controller of the expanded structure is given. A numerical example shows the effectiveness of the method proposed.