Construction of Lyapunov-Krasovskii functionals for a class of nonlinear difference systems with delay

Nonlinear systems of difference equations with delay and nonlinearities of a sector type are studied. New constructions of Lyapunov-Krasovskii functionals are proposed for such sys-tems. With the aid of these functionals, conditions are obtained under which solutions of the considered systems are uniformly ultimately bounded for any value of delay. An example is given to demonstrate the effectiveness of the proposed approaches.