Use of canonical forms of linear control systems for stabilization of periodic solutions

The problem of stabilization of a periodic solution to a nonlinear differen tial system by an additional force is studied. The method of investigation is based on the reduction of the equation in variations to a canonical form (scalar equation of nth order). Therefore. first. conditions of existence of such form with respect to the group of linear periodic transformations a re given and, then, it is established that, if a system in variations posse sses a canonical form then the periodic solution is stabilized to an expone ntially stable one with a prescribed exponent.