The group and Riesz basis properties of string systems with time delay and exact controllability with boundary control

摘要

The group property of a string system with time delay in boundary and the Riesz basis property of eigenvectors of the system are discussed in the present paper. It is proved that, when the feedback with delay t > 0, the system also associates a Co group, and its eigenvectors (generalized eigenvectors) form a Riesz basis in Hilbert space H. This result shows that time delay may destroy the stability of the system, but the group and Riesz basis properties are kept. Asa consequence, the exact controllability of the system with boundary control is given.