连续区间系统的鲁棒H_∞控制:LMI方法  

Robust H_∞ Control for the Continuous-time Interval System:an LMI Approach

作　　者：张达敏[1] 张霄力[1] 

机构地区：[1]厦门大学信息科学与技术学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2009年第5期651-655,共5页Journal of Xiamen University：Natural Science

基　　金：福建省青年科技人才创新项目(2005J006)资助

摘　　要：研究了一类连续区间系统的鲁棒H∞控制问题.首先基于一个等价变换,将区间系统转换为一个具有时变参数不确定性的线性系统.然后利用线性矩阵不等式(LMI)方法讨论了系统的鲁棒稳定性以及扰动衰减度,得到检验该类系统鲁棒稳定且具有H∞性能γ的新的充分条件,用同样的方法得到系统鲁棒镇定且具有H∞性能γ的判定条件,并设计了系统鲁棒H∞状态反馈控制器.通过求解一个凸优化问题,还可以得到该区间控制系统最优的扰动抑制水平及相应的鲁棒H∞状态反馈控制器.所得结果均以LMI的形式给出,求解方便.最后通过仿真算例验证了本文结果具有更小的保守性.This paper studies the robust H∞ control for the continuous-time interval system. Firstly, based on an equivalent transformation, the continuous-time interval system is converted into a linear system with time-varying uncertainties. Then the robust stability conditions along with disturbance attenuation level are discussed by employing LMI approach. Some new sufficient results are gained in terms of linear matrix inequalities （LMI）. With these results,it is easy to test the robust stability or stabilizability as well as the disturbance attenuation level. Using the same method,the robust H∞ controller for stabilizing the interval system is designed. By solving the convex optimization problem, the optimal disturbance attenuation level and the corresponding optimal robust H∞ state feedback control law can also be obtained. At the end of the paper,some numerical examples are given to show that our results in this paper are less conservative than the existing ones.

关 键 词：区间系统 鲁棒H∞控制 状态反馈 LMI方法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]