Stability of neutral delay-differential systems: Boundary criteria (Q1126611)

For linear neutral delay differential equations of the form \[ \dot{x}(t)=Ax(t)+Bx(t-\tau)+C\dot{x}(t-\tau), \] where \(x:{\mathbb{R}}_+\to{\mathbb{R}}^n\) is an unknown function, \(A\), \(B\) and \(C\) are constant \(n\times n\)-matrices and \(\tau=\text{ const}>0\), a series of delay dependent asymptotical stability criteria are given. The criteria are based on the evaluation of a real-valued function on the boundary of a rectangle in the complex plane.