Asymptotic stability of neutral differential systems with many delays (Q555432)

The authors consider the linear system of neutral differential equations with several delays \[ \begin{cases} y'(t) = Ly(t) + \sum_{j=1}^d M_j y(t-\tau_j) + \sum_{j=1}^d N_j y'(t-\tau_j)\;,\quad t>0,\\ y(t) = \varphi(t)\;,\quad t\leq 0\;, \end{cases} \] where \(L\), \(M_j\), \(N_j\in\mathbb C^{N\times N}\), \(j=1,\dots,d\), are complex matrices, \(\tau_j>0\), \(j=1,\dots,d\), are constant delays, and \(\varphi(t)\) is a continuously differentiable \(\mathbb R^N\)-valued function. Some necessary and sufficient conditions for the asymptotic stability of the system are established.