一类离散综合控制系统的保性能控制  

Guaranteed cost control for a class of discrete integrated control system

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]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《东北师大学报（自然科学版）》2022年第3期44-50,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：基于前期连续系统理论,利用李亚普诺夫稳定性理论、矩阵分析方法以及新的交叉向界定方法,构造了新的性能指标和新的李亚普诺夫泛函,对于不确定时滞离散奇异摄动控制系统进行了研究.给出了时滞依赖和时滞独立两种情况下的保性能控制器,推出了较小的性能指标上界.指出了在零到奇异摄动上界的整个区间范围内系统渐近稳定,缩小了上界、扩大了保性能控制区域.最后,用数值样例验证了结论的可行性和有效性,通过对比相关文献,展示了本文定理方法的优越性.Based on the existing continuous system theoretical results,utilizing Lyapunov stability theory to research the guaranteed cost control problem of uncertain discrete-time singularly perturbed control systems with time delay by means of linear matrix analysis method and the new cross-term defined method,a new definition to the performance index is constructed out as well as a new selected Lyapunov functional is given.Meanwhile,combing with the lemmas,matrix analysis method and linear matrix inequality method and so on,the sufficient criterias of the guaranteed cost controller both delay dependence and delay independence are obtained,and to deduce a smaller upper bound of performance index.It is pointed out that the system is asymptotically stable in the whole range from zero to the upper bound of singular perturbation,the reduced upper bound of performance index and the extended guaranteed cost control range are showed.At last,the enumerated examples are showed to illustrate the feasibility and effectiveness of the consequential conclusion,the superiority of the derived theorem control method is reflected by comparing the relevant literatures.

关 键 词：保性能控制 不确定离散时滞系统 性能指标 交叉项界定方法 李亚普诺夫泛函 

分 类 号：O231.2[理学—运筹学与控制论]