Algebraic stability criteria of linear neutral systems with multiple time delays (Q1883523)

In this interesting paper, based on the characteristic equation approach, the authors study the asymptotic stability of linear neutral delay differential systems with multiple time delays of the form \[ x'(t)=Ax(t)+\sum_{j=1}^m[B_jx(t-\tau_j)+C_jx'(t-\tau_j)], \] where \(x(t)\in C^{n\times 1}\) is the complex state vector, the constant parameters \(\tau_j\geq 0\) with \(\tau=\max\{\tau_j,\;j=1,2,\dots,m\}\) represent the delay arguments and with \(A, B_j, C_j\in C^{n\times n}\), \(j=1,2,\dots,m\). The matrix \(A\) is assumed to be a Huiwitz matrix, that is all eigenvalues of \(A\) have negative real parts. Simple delay-independent algebraic criteria are established in terms of the spectral radius of the modulus matrices, which are easy to check via Routh-Hurwitz and Schur-Cohn criteria.