不确定变时滞奇异摄动系统的控制器设计  

Controller Design for Singularly Perturbed Systems with Uncertain Time-Varying Delay

作　　者：孙凤琪[1] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《吉林大学学报（理学版）》2017年第6期1449-1455,共7页Journal of Jilin University:Science Edition

基　　金：中国高校基本科研业务费专项基金(批准号:N100406010)

摘　　要：采用鲁棒控制器的设计技术及鲁棒二次可镇定控制器的设计思想,对闭环系统进行鲁棒控制,以消除时滞因素和不确定性对实际系统的不良影响.通过构造一种新的Lyapunov泛函,给出基于线性矩阵不等式形式的时滞依赖和时滞独立的控制器设计方法.结果表明,设计的状态反馈控制器,能使闭环系统在不确定性的容许变化范围内达到性能要求,降低了系统的灵敏度.数值算例表明,所得结果更具有普遍性,可应用于带有不确定项的时变时滞非标准型系统.With the design technique of robust controller and the design idea of robust quadratic stabilization controller,robust control of the closed-loop system was carried out to eliminate the adverse effects of delay factors and uncertainties on the actual system.By constructing a new Lyapunov functional,the author proposed design method of delay-dependent and delay-independent controller based on linear matrix inequality.The results show that the designed state feedback controller can make the closed-loop system satisfy the performance requirements within the allowable range of uncertainty,and reduce the sensitivity of the system.Numerical results show that the obtained results are more universal and can be applied to the non-standard systems with uncertain time-varying delay.

关 键 词：奇异摄动系统 线性矩阵不等式 时变时滞 鲁棒控制 时滞依赖 时滞独立 LYAPUNOV-KRASOVSKII泛函 

分 类 号：O23[理学—运筹学与控制论]