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 discrete-time 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 time-invariant. 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.