Controllability of nonlinear delay oscillating systems
MetadataShow full item record
This item's downloads: 0 (view details)
Liang, Chengbin; Wang, JinRong; O'Regan, Donal (2017). Controllability of nonlinear delay oscillating systems. Electronic Journal of Qualitative Theory of Differential Equations (47),
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.