2017
Том 69
№ 9

All Issues

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

Barkhayev P. Yu., Rabah R., Sklyar G. M.


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.

Citation Example: Barkhayev P. Yu., Rabah R., Sklyar G. M. On the problem of exact controllability of neutral systems with time delay // Ukr. Mat. Zh. - 2016. - 68, № 6. - pp. 800-815.