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We study a method associated with constructing of delayed feedback for local stabilization of periodic orbits of nonlinear discrete systems. An alternative approach to the construction of characteristic polynomial for the delay system linearized in the neighborhood of T -cycle is suggested. It is proven that our new alternative approach is equivalent to the standard one, however, it allows us to produce directly new forms of polynomials. These forms are convenient in applications to thedoi:10.21638/11701/spbu10.2016.410 fatcat:4mkj57wk2nbptcayc5umegjs4i