Journal
EUROPEAN JOURNAL OF CONTROL
Volume 38, Issue -, Pages 39-46Publisher
ELSEVIER
DOI: 10.1016/j.ejcon.2017.08.002
Keywords
Relative controllability; Delay Grammian matrix; Delay differential systems
Categories
Funding
- National Natural Science Foundation of China [11661016]
- Training Object of High Level and Innovative Talents of Guizhou Province [(2016)4006]
- Unite Foundation of Guizhou Province [[2015]7640]
- Graduate Course of Guizhou University [ZDKC[2015]003]
- Slovak Research and Development Agency [APW-14-0378]
- Slovak Grant Agency VEGA [2/0153/16, 1/0078/17]
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This paper is devoted to analysis of relative controllability of semilinear delay differential systems with linear parts defined by permutable matrices. By introducing a notion of delay Grammian matrix, we give a sufficient and necessary condition to examine that a linear delay controlled system is relatively controllable, which is a generalized criterion for the classical linear controlled systems without delay. Thereafter, we construct a suitable control function for semilinear delay controlled system, which admits us to following the framework of fixed point methods to consider the same issue. More precisely, we apply Krasnoselskii's fixed point theorem to derive a relative controllability result for semilinear delay controlled systems. Finally, two numerical examples are presented to illustrate our theoretical results with the help of computing the desired control functions and inverse of delay Grammian matrix as well. (C) 2017 European Control Association. Published by Elsevier Ltd. All rights reserved.
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