On the stability of linear systems with delay

The stability of a system governed by the equation with delay constants were determined by the stability of the quasi-polynomial. It was shown that the stability analysis of quasi-polynomial can be reduced to the stability analysis of certain family of polynomials. It was also considered that at zero delays the delay constant becomes a stable polynomial, to determine the stability domain of system. The stability conditions in the second and fourth-order principle minors were found positive. The actual stability domain constructed by integrating the equations of the system differs very less from the estimated one.