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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。
For linear neutral delay system, the output feedback controller design is based on the spectral decomposition theory of linear operator semigroups. Under the condition that the system satisfies the limited number of unstable eigenvalues, the phase space of infinite dimensional system solution is decomposed into finite dimensional unstable generalized feature subspace and infinite dimensional stable generalized feature subspace using the theory of spectra and projection operator. Straight and straight. Then the auxiliary operator is referenced and the output feedback control law is obtained by using infinitesimal generators of semigroups of linear operators. The asymptotic stability of closed-loop feedback control system is also proved. Numerical experiments verify the effectiveness of the proposed method.