Pole Assignment to Echo Feedback Concerning Two Order Distributed Parameter Systems

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 are given by the operator in the constructive semi-scalar functions with the single pole.