Feedback equivalence and global stabilization of nonstationary discrte systems

A problem is considered for the global stabilization of nonstationary nonlinear discrete systems without outputs. Here, the key instant is the establishment of equivalence of an arbitrary discrete system and a lossless system with the use of the appropriate feedback. The construction of control laws is performed on the basis of new methods for investigating the stability of nonautonomous systems of difference equations, using the theory of limit systems and Lyapunov limit functions.