Lyapunov functions for nonlinear discrete-time control systems

For nonlinear discrete time control systems the classes of Lyapunov functions are identified which establish the necessary and sufficient conditions of absolute stability in the case of nonstationary nonlinear characteristics having sectoral constraints. An algebraical criterion is obtained of absolute stability if or discrete-time systems. These results are extended to a totality of linear nonstationary discrete-time systems and difference nesting of a specific form.