不确定广义系统的鲁棒H_2控制

Robust H_2 Control for Uncertain Generalized Systems

利用线性矩阵不等式 (LMI)方法 ,研究范数有界的不确定广义系统的鲁棒H2 性能分析与控制问题。对该系统所有容许的不确定参数 ,提出了满足鲁棒H2 次优性能的一个线性矩阵不等式 (LMI)的充分条件。进而设计了一个状态反馈控制律 ,保证了闭环系统是容许的且满足鲁棒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。利用Matlab控制工具箱 ,给出了该控制律的LMI实用设计方法。

The problems of robust H \-2 performance analysis and control for generalized systems with norm-bounded uncertainties are studied using linear matrix inequality(LMI) approach. A sufficient condition for linear matrix inequalities is presented such that the systems satisfy the robust H \-2 suboptimal performance for all admissible uncertainties. Furthermore, a state feedback controller is designed, which guarantees that the resulting closed-loop system is admissible and satisfies the robust H \-2 suboptimal performance, that is, the H \-2 norm of the closed-loop system is less than a given positive number. An efficient LMI method for designing the controller is given using Matlab toolbox.Finally, a numerical example is given to illustrate the results.