Delay Dependent Stability of High Order Neutral Systems with Multiple Delays

This paper investigates the stability of high order neutral systems in the presence of multiple delays. A stability test is derived using the distribution of the roots of its associated characteristic equation. An analytical formula is derived to compute finite unstable characteristic roots for different delay parameters using the argument principle, modulus properties and boundary conditions. The radius of semicircle (contour) is obtained in the right half of complex plane, which engulfs all the finite roots (unstable) of the delay system. The proposed approach is demonstrated on a mass-spring-damper vibration controlled system and a numerical example. The results are validated with the standard stability tests.