Input and output decoupling zeros of linear periodic discrete-time systems

The notions of input and output decoupling zeros are extended to a linear periodic discretetime system. The ordered sets of structural indices are also analyzed for these notions and for the notions of invariant zero, transmission zero, eigenvalue and pole of such a system. For any non-zero zero, eigenvalue and pole, the corresponding ordered set of structural indices is timeinvariant. The input decoupling zeros, the invariant zeros and their ordered sets of structural indices are not altered by a linear periodic state feedback. New characterizations of the zeros, eigenvalues and poles are introduced through a time-invariant matrix mechanism, which is related with the periodic matrices describing the system more directly than the associated system.