A stability criterion for the system of high-order neutral delay differential equations

We study the delay–dependent stability of linear high-order delay differential systems of neutral type. We firstly derive a bound of the unstable eigenvalues of the neutral systems. The bound of the unstable eigenvalues involves only the norms of the matrices of lower size. Then, using the argument principle, we present some stability criterion that is a necessary and sufficient condition for the delay–dependent stability of the neutral systems. Furthermore, we provide an efficient numerical algorithm for checking the stability of the neutral systems. Some numerical examples are given to illustrate the main results which extend those in the literature.