On the relative controllability of neutral delay differential equations

In this paper, we study a class of neutral time-delay control systems. The relative controllability of the linear system is given by constructing the corresponding neutral delay Gramian matrix and adopting the classical analysis idea. Next, we use Krasnoselskii's fixed point theorem to show that the semilinear system is relatively controllable under the mild condition. Finally, we give two numerical examples to verify the theoretical results.