广义Delta算子系统的H_∞性能分析及控制  

H_∞ Performance Analysis and Control of Singular Delta Operator Systems

作　　者：刘琳[1] 董心壮[1] 齐春明 

机构地区：[1]青岛大学自动化工程学院,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2014年第4期13-17,22,共6页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金项目资助(61104001)

摘　　要：针对广义Delta算子系统的H∞性能分析及H∞控制问题,本文采用Delta算子方法,利用线性矩阵不等式,对广义Delta算子系统进行H∞性能分析。通过分析得到使广义Delta算子系统容许且具有H∞性能的充分必要条件。在此基础上,进一步考虑了广义Delta算子系统的H∞控制问题,对于不是容许且具有指定H∞性能的广义Delta算子系统,基于线性矩阵不等式,给出了广义Delta算子系统状态反馈H∞控制器的存在条件和设计方法,并利用MATLAB-LMI工具箱,对给出的数值算例进行计算和分析。结果表明,所得闭环广义离散系统容许且满足H∞性能,证明了本文所给出的判别方法的有效性。Delta算子方法在广义离散系统的性能研究中可以良好应用。Aiming at the problems of H∞ performance analysis and H∞ control of singular delta operator systems,this paper applies the method of Delta operator and linear matrix inequality to analyze H∞ performance for the linear singular Delta operator system.In the analysis,a necessary and sufficient condition is given,such that a singular delta operator system is admissible and satisfies a prescribed H∞ performance.Then based on the above results,we further considered the problem of H∞ control for the linear singular Delta operator system.And for these singular Delta operator systems without admissibility and satisfying H∞ performance,the existence condition and design method of a suitable state feedback H∞ controller are obtained for singular delta operator systems based on linear matrix inequality.Finally,we take some numerical systems for examples.After calculating and analyzing by using MATLAB-LMI tools,these results show that the closed-loop system we get is admissible and satisfying prescribed H∞ performance.It suggests that these proposed results are effective.Also,the Delta operator method can be well used in the research of many properties of singular discrete systems.

关 键 词：广义系统 DELTA算子 H∞控制 线性矩阵不等式 

分 类 号：O231[理学—运筹学与控制论]