Kyrashchuk D. Structurization and stability investigation dynamic systems of discrete argument

Structurization and stability investigation dynamic systems of discrete argument. In this thesis, the structurization some classes nonlinear discrete systems to the uniform fractional-rational view is made. Use the method of Lapunov functions to nonlinear difference systems with delay is proofed. Obtained result is used for investigation systems of linear difference equations huge dimension and systems of nonlinear difference equations with fractional-rational right hand side. Conditions stability systems of linear difference equations with delay are obtained by use the method of functional of Lyapunov-Krasovsky quadratic view . The estimations of characteristics of transitional process systems of linear difference equations with delay are calculated. The method construction optimal functional of Lyapunov-Krasovsky for obtaining guaranteeing conditions stability in class of functionals of quadratic view is made.