基于扩展LMI的多目标H_2/H_∞状态反馈控制综合

Multi-objective H2/H∞ state-feedback control synthesis based on extended LMI characterizations

对于连续时间系统的多目标H2／H∞控制问题通过状态反馈给出了一个新的综合方法。该方法依赖于引入的附加变量,降低了通常条件下基于LMI的多目标控制问题的保守性。新方法应用消去引理(Elimination Lemma)得出扩展的H2性能和H∞性能的LMI约束条件,使得与控制器参数相关的优化变量和系统矩阵之间是独立的,能够使用不同的Lyapunov矩阵变量来处理多目标控制问题,仿真结果验证了新方法的有效性。

A synthesis method for the multi-objective H2/H∞ synthesis problem via state feedback is proposed in the continuous-time setting. This newly proposed procedure relies on the introduction of new extra variables and allows reducing the conservatism under the usual existing conditions for the multi-objective control problem based on LMI. On the ground of the Elimination Lemma, this method gives the extended LMI constraint conditions of the H2 performance and the H∞ performance, which make optimization variables associated with the controller parameters independent of the system matrices, and lead to the use of two different Lyapunov functions to deal with the multi-objective control problem. The numerical simulations prove the validity of this design framework.