On the stability of a class of essentially nonlinear difference systems

Abstract

The problem of the zero solution stability for a certain class of essentially nonlinear difference systems is studied. Theorems on the stability by the inhomogeneous approximation are proved. Systems of triangular form are considered as systems of nonlinear approximation. Conditions under which perturbations do not destroy stability of the zero solution are formulated in the form of the inequalities establishing relation between orders of perturbations and homogeneity of functions, entering into the system of nonlinear approximation.