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Öğe Asymptotic stability of solutions to perturbed linear difference equations with periodic coefficients(2002) Aydin K.; Bulgak H.; Demidenko G.V.We consider perturbed linear systems of difference equations with periodic coefficients. The zero solution of a nonperturbed system is assumed asymptotically stable, i.e., all eigenvalues of the monodromy matrix belong to the unit disk {|?| < 1}. We obtain conditions on the perturbation of this system under which the zero solution of the system is asymptotically stable and also establish continuous dependence of one class of numeric characteristics of asymptotic stability of solutions on the coefficients of the system.Öğe An estimate for the attraction domains of difference equations with periodic linear terms(2004) Aydin K.; Bulgak H.; Demidenko G.V.We consider the quasilinear systems of difference equations with periodic coefficients in linear terms. We obtain estimates for the attraction domain of the zero solution and establish inequalities for the norms of solutions. The results are stated in terms of Lyapunov-type matrix series.
