Mathematical Modeling

On the stability of a class of essentially nonlinear difference systems

A. A. Sultanbekov

St. Petersburg State University, Saint-Petersburg, Russia

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.

Keywords: difference systems, asymptotic stability, Lyapunov's functions.

UDC: 517.962.2

MSC: Primary 37C75; Secondary 93D05

Original article submitted 14/IX/2011
revision submitted – 30/V/2012

DOI: 10.14498/vsgtu998

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