On the problem of exact controllability of neutral systems with time delay

Abstract

We study the problem of exact controllability for a broad class of neutral and mixed systems with time delay. We consider an equivalent operator model in a Hilbert space and formulate steering conditions for controllable states in the form of a vector moment problem. The existence of a basis of eigenvectors of the operator of system with delay significantly simplifies the form of the moment problem. A change of function in the control by a feedback law modi es the system structure in order to guarantee the existence of a basis of eigenvectors of the corresponding operator. We prove a criterion for the exact controllability and determine the exact critical time of control.