Stability on a class of linear neutral differential systems with distributed argument (Q2721540)

The authors consider the linear neutral differential system NEWLINE\[NEWLINE \frac{d}{dt}\left[x_i(t)-\int_{a_i}^{b_i}x_i(t-\theta) d\alpha _{i}(t, \theta)\right] +\sum_{j=1}^{n}\int_{c_{ij}}^{d_{ij}}x_j(t-s) d\beta _{ij}(t, s)=0,\quad i=1, 2, \dots, n, NEWLINE\]NEWLINE where \(a_i, b_i, c_{ij}, d_{ij}\in (0, \infty)\) are constants with \(a_i=0\) and fixed \(\theta\) and \(s\), and for every \(t\geq t_0\) they are positive bounded variations in \(\theta\) and \(s\), respectively, \(i,j=1, 2, \dots, n\). Sufficient conditions are obtained for the zero solution to the system to be uniformly stable as well as asymptotically stable.