Controllability of nonlinear delay oscillating systems

By Chengbin Liang, Jinrong Wang, Donal O'Regan. 2017

50 citations recorded by the source corpus.

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.

Subfields: Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6ce37d4f67119712903683fe1b0d9d9f4a8c2ac8

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In Numerical Analysis

1. Amar Debbouche
2. Jinrong Wang
3. Yong Zhou

Citations in the corpus

• Relative controllability in fractional differential equations with pure delay (2018, background): “System (3) is relatively controllable if and only if x1 > (n − 1)τ and rank Sn = n.”