受控正时滞系统的弹性静态输出反馈镇定  

Resilient static output feedback stabilization for controlled positive time-delay systems

作　　者：李振波[1] 朱淑倩[2] 

机构地区：[1]山东经济学院统计与数学学院,山东济南250014 [2]山东大学数学学院,山东济南250100

出　　处：《山东大学学报（工学版）》2011年第3期46-51,58,共7页Journal of Shandong University（Engineering Science）

基　　金：国家自然科学基金资助项目(61004011)

摘　　要：研究了具有区间不确定性的受控正时滞系统的弹性静态输出反馈镇定问题。通过引入一个小的标量,得到了正时滞系统渐近稳定的一个充要条件,使得Lyapunov矩阵与系统矩阵得以分离,从而更利于输出反馈控制器的设计。基于此条件并利用矩阵不等式技术,针对控制矩阵的不同情形,给出了具有区间加性摄动的弹性控制器存在的充要/充分条件及具体表达式,其中控制器增益矩阵可利用锥补线性化技巧进行有效地求解。数值算例表明了设计方法的有效性。The problem of resilient static output feedback stabilization was investigated for controlled positive time-delay systems with interval uncertainties.By introducing a small scalar,a necessary and sufficient condition was obtained for the asymptotical stability of positive time-delay systems,which was more useful when designing output feedback controllers since the Lyapunov matrix was separated from the system matrices.Based on the above condition and by utilizing the technique of matrix inequality,for different cases of the control matrix,necessary and sufficient/sufficient conditions were established for the existence of the resilient controller with interval additive gain variation and detailed expressions of the controller were also given.The desired controller gain matrices could be effectively determined via cone complementarity linearization techniques.A numerical example was presented to illustrate the effectiveness of the proposed method.

关 键 词：正系统 时滞系统 输出反馈镇定 弹性控制 锥补线性化 

分 类 号：O231[理学—运筹学与控制论]