Multiplicative stability criteria based on difference solutions of ordinary differential equations

For computer analysis of Lyapunov stability, multiplicative criteria are proposed that are based on difference approximations to solutions of the Cauchy problem. These criteria can be applied to ordinary differential equations in normal form and include the necessary and sufficient stability conditions. For a system of linear equations with constant coefficients, information on the characteristic polynomial of the coefficient matrix and its roots is not used. The stability analysis is combined with difference solution and simulation of error accumulation. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 127–142, January–February 2006.