基于线性矩阵不等式的广义系统H_2优化控制

H_2 Optimal Control for Descriptor Systems Based on LMI

研究了线性时不变连续广义系统的H2 优化控制问题 ,目的是寻找一个状态反馈控制器 ,不仅保证闭环系统是容许的 ,而且使闭环系统达到H2 次优性能 ,即闭环传递函数的H2 范数小于一个给定的正数γ·利用线性矩阵不等式 (LMI)方法得到该系统的H2 范数界的一个充分条件 ,并给出了一个H2 次优控制器的设计·数值例子进一步说明了设计方法·

The H 2 optimal control for linear time-invariant continuous-time descriptor systems was studied. A state feedback controller was designed. The resulting closed-loop system is admissible and satisfies the H 2 suboptimal performance,that is,the H 2 norm of the closed-loop system is small than a given positive number γ. A sufficient condition that the H 2 norm is bounded was presented,and a H 2 suboptimal controller was designed using the method of LMI. A numerical example was given to illustrate the design approach.