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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 6, pp. 800–815, June, 2016.
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Rabah, R., Sklyar, G.M. & Barkhayev, P.Y. On Exact Controllability of Time-Delay Systems of Neutral Type. Ukr Math J 68, 910–927 (2016). https://doi.org/10.1007/s11253-016-1265-7
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DOI: https://doi.org/10.1007/s11253-016-1265-7