Algebraic criteria for stability of linear neutral systems with a single delay (Q5949509)

A linear neutral delay-differential system NEWLINE\[NEWLINE \dot x(t)=Ax(t)+Bx(t-\tau)+C\dot x(t-\tau) NEWLINE\]NEWLINE is considered, where \(A,~ B\) and \(C\) are real constant \(n\times n\)-matrices, and \(\tau\) is a positive constant. The stability of such systems via Routh-Hurwitz and Schur-Cohn criteria is investigated. Some algebraic criteria for delay-independent stability are presented. These criteria may complement those reported in the literature. The theoretical results are illustrated by examples.