In this paper, we consider the issue of diagonal stability for a class of matrices of a special type. The conditions for matrix diagonal stability are related to the conditions for the asymptotic stability of difference-differential equations. The choice of a special type of matrices is due to the problem of equidistant deployment of a group of mobile agents. In this paper, we obtain conditions guaranteeing diagonal stability for the considered class of matrices. An algorithm was also found for constructing the Lyapunov-Krasovsky quadratic functional for the corresponding system with delay.