A Condition Of A Closed-loop System To Form Riesz Basis

Let .4 be the infinitesimal generator of a Co-semigroup T = {T(t)}t≥0 on the Hilbert space X. Input operator B and output operator C may be unbounded linear operators in the infinite-dimensional Hilbert space. In this paper, we deal with Riesz basis of the following open-loop system ∑(A, B, C, D)with the feedbacku(t) = Ky(t) + v(t).We study the transfer function of the system to discuss the spectral distribution of the closed-loop system. Using the perturbation theory for basis, we give a sufficient condition which ensures all the generalized eigenvectors of the closed-loop system to form a Riesz basis. Finally, two typical examples are presented to illustrate the application of our result.