  We explore the problem of stabilization of unstable periodic orbits in
discrete nonlinear dynamical systems. This work proposes the generalization of
predictive control method for resolving the stabilization problem. Our method
embodies the development of control method proposed by B.T. Polyak. The control
we propose uses a linear (convex) combination of iterated functions. With the
proposed method auxiliary, the problem of robust cycle stabilization for
various cases of its multipliers localization is solved. An algorithm for
finding a given length cycle when its multipliers are known is described as a
particular case of our method application. Also, we present numerical
simulation results for some well-known mappings and the possibility of further
generalization of this method.
