Abstract: To analyse the absolute stability of nonlinear impulsive systems are proposed recurrent mathematical expressions derived from the criterion of absolute stability and allows by means of the developed program to determine the coecients of a special polynomial obtained from the transfer function of a nonlinear pulse system of any order. The technique of checking the strict positivity of the obtained polynomial (which is analogous to the characteristic polynomial of the system) the signs of the determinants inerney matrix and thereby detect the absolute stability of the system. Determinants of innoref are computed by an efficient algorithm for double triangularization, giving the win to 2 – 4 times compared to the classical algorithm of Gauss

Keywords: nonlinear pulse systems, the calculation of the coefficients of the polynomial, the construction innerы matrices, determining the absolute stability of the signs of the determinants of Insarov.