无记忆状态反馈广义H_(2)控制  

Memoryless state feedback generalized H_(2)control

作　　者：孙凤琪[1] SUN Feng-qi(College of Mathematics and Computer,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《东北师大学报（自然科学版）》2023年第4期39-45,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61741318).

摘　　要：对系统存在无记忆状态广义控制器进行了理论深化,讨论了时滞依赖和时滞独立2种情形下,无记忆状态广义H_(2)控制器存在的充分性判别条件和具体设计方法.设计了一个无记忆状态广义H_(2)控制器,采用新的引理,推出了保守性相对更小的稳定性判据.对所得结论进行了线性化处理,用数值样例验证了本文所得结论的有效性和可行性.指出在零到奇异摄动上界的整个区间范围内,闭环系统渐近稳定,扩大了广义H_(2)稳定空间,缩小了L_(2)-L_(∞)性能指标.通过与相关文献进行稳定态指标对比,本文所得方法具有一定的优越性和较小的保守性,并且适用于标准和非标准情形.To deepen the theory and discuss the sufficient conditions for the existence of memoryless state generalized H_(2)controller in both cases of delay dependence and delay independence,the specific designed method of memoryless state generalized controller for the system is given by using the new lemmas,meanwhile the stability criterion with less conservatism is introduced.The obtained conclusions are linearized and theselectednumerical example verifies the effectiveness and feasibility for the obtained conclusions.It is pointed out that the closed-loop system is asymptotically stable in the whole interval from zero to the upper bound of the singular perturbation,which expands the generalized stability space and reduces the L_(2)-L_(∞)performance index.By comparing the stability index with the relevant literature,to show the certain advantages and less conservatism of the chosen method,that is suitable for standard and non-standard cases in this treatise.

关 键 词：鲁棒稳定性 广义H_(2)控制 L_(2)-L_(∞)性能指标 交叉项界定法 线性矩阵不等式 

分 类 号：O231.2[理学—运筹学与控制论]