中文摘要：

讨论了二阶分布参数系统反射反馈的极点配置问题，即在二阶发展方程描述的控制系统中，考虑反射控制律反馈的闭环控制系统的反本征值问题；在复可分的Hilbert空间中，将算子的非零单重的二次本征值问题转化为算子扰动的一次本征值问题，获得了本征值是内积方程的根这一重要结果，在构造的单重极点的半纯函数得到了问题的解和解的构造性表达式.

英文摘要：

Abstract Pole assignment to echo feedback concerning two order distributed parameter systems is discussed. Firstly, the anti-eigenvalue problem on the closed-loop control system of second order evolution equation with echo feedback is described. In a separable and complex Hilbert space, the operator＇s nonzero single quadratic eigenvalue problem is transformed into the simple eigenvalue problem on the operator with perturbation. Therefore, the important result that the eigenvalue is the root of the inner product equation is obtained. The solutions of the problem and the constructive expression of the solutions arc given by the operator in the constructive semi-scalar functions with the single pole.