On Exact Controllability of Time-Delay Systems of Neutral Type

We study the problem of exact controllability for a broad class of neutral and mixed time-delay systems. We consider an equivalent operator model in a Hilbert space and formulate steering conditions for controllable states as a vector moment problem. The existence of a basis of eigenvectors of the operator of system enables us to significantly simplify the form of the moment problem. A modification of control by a feedback law affects the structure of the system with an aim to guarantee the existence of a basis of eigenvectors of the corresponding operator. We prove a criterion of exact controllability and determine the precise critical time of controllability.