基于算子半群的中立型延时系统反馈控制  

Feedback Control for Neutral Delay Systems Based on Linear Operator Semigroup

作　　者：郝智红[1] 崔家瑞[2] 

机构地区：[1]国家开放大学理工教学部,北京100039 [2]北京科技大学自动化学院,北京100083

出　　处：《控制工程》2017年第6期1175-1179,共5页Control Engineering of China

基　　金：国家高技术研究发展计划(863计划)(2012AA050209)

摘　　要：针对线性中立型延时系统,利用线性算子半群的谱分解理论进行输出反馈控制器设计。在系统满足不稳定特征根个数有限的条件下,利用谱理论并结合投影算子,将无穷维系统解的相空间分解为有限维不稳定广义特征子空间和无限维稳定广义特征子空间的直和。进而引用辅助算子,并利用线性算子半群的无穷小生成元得到输出反馈控制律,并证明了反馈控制闭环系统的渐近稳定性。数值实验证实了所提设计方法的有效性。Output feedback controller design is investigated based on spectral decomposition of linear operator semigroup for linear neutral delay systems （NDSs）. Under conditions of system with finite unstable characteristic roots, by the spectral theory and the projection operator, the infinite dimensional phase space of system solutions is decomposed to the direct sum of finite-dimensional unstable generalized eigensubspaces and infinite dimensional stable generalized eigensubspaces. Then the control law of output feedback is obtained by the infinitesimal generator of linear operator semigroup. And the asymptotic stability of the closed loop system with output feedback control is proved. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design approach.

关 键 词：中立型延时系统 线性算子半群 谱分解 输出反馈控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]