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    Controllability of nonlinear delay oscillating systems

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    Date
    2017-01-01
    Author
    Liang, Chengbin
    Wang, JinRong
    O'Regan, Donal
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    Recommended Citation
    Liang, Chengbin; Wang, JinRong; O'Regan, Donal (2017). Controllability of nonlinear delay oscillating systems. Electronic Journal of Qualitative Theory of Differential Equations (47),
    Published Version
    https://doi.org/10.14232/ejqtde.2017.1.47
    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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    http://hdl.handle.net/10379/12447
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    • Externally hosted open access publications with NUI Galway authors (2)
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