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Controllability of nonlinear delay oscillating systems

Liang, Chengbin
; 
Wang, JinRong
; 
O'Regan, Donal
Identifiers
http://hdl.handle.net/10379/12447
 https://doi.org/10.13025/25091
Publication Date
2017-01-01
Keywords
controllability, delay gramian matrix, control function, delay oscillating systems, pairwise permutable matrices, linear discrete-systems, pure delay, differential-equations, constant-coefficients, stability, representation, parts
Type
Article
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Citation
Liang, Chengbin; Wang, JinRong; O'Regan, Donal (2017). Controllability of nonlinear delay oscillating systems. Electronic Journal of Qualitative Theory of Differential Equations (47),
Abstract
In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.
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Publisher
University of Szeged
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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