基于谱分解的中立型延时系统控制器设计

Controller Based on Spectral Decomposition for Neutral Delay Systems

针对线性中立型延时系统,提出一种基于算子半群谱分解理论的控制器设计方法.在中立型项的范数小于1的情况下,利用谱理论并结合投影算子,将系统无穷维解空间分解为有限维不稳定广义特征子空间和无限维稳定子空间的直和.通过对有限维子系统的研究,得到系统状态反馈控制律,并通过投影算子证明了状态反馈控制闭环系统的渐近稳定性.最后数值例子验证了所提方法的有效性.

A controller design is proposed based on spectral decomposition of operator semigroup for linear neutral delay systems （NDSs）. When the norm of the neutral term is less than one, by spectral theory and projection operator, the infinite dimensional solution space of system is decomposed into the direct sum of finite dimensional unstable generalized eigensubspace and infinite dimensional stable subspace. Then for the finite dimensional subsystem, the control law of state feedback is obtained. And the asymptotic stability of the colsed loop system with state feedback control is proved by the projection operator. Finally, a numerical example demonstrates the effectiveness of the proposed approach.