Stability of linear neutral systems with multiple delays: Boundary criteria. (Q1421265)

The linear neutral delay-differential system with multiple delays \[ \frac{dx}{dt}=A(t)+\sum_{j=1}^m\left(B_jx(t-\tau_j)+C_j\frac{dx(t- \tau_j)}{dt}\right) \] is considered, where \(x(t)\) is assumed to be a function \(\mathbb{R}_+\to \mathbb{R}^n\), \(A, B_j,\) and \(C_j\in \mathbb{R}^{n\times n}\) are constant matrices and \(\tau_j\), \(j=1,\dots,m\), are positive constant delays. In the present paper, delay-dependent criteria for the stability of the above system are established.