On the inner and outer poles and zeros of a linear time-varying system

The notion of inner and outer poles and zeros of a linear time-varying discrete-time system is developed in terms of noncommutative factorizations of operator polynomials with time-varying coefficients. Emphasis is placed on left and right poles and zeros, which are referred to as outer poles and zeros. The outer poles and zeros arise in the study of system reducibility, stability, and transmission blocking zeros. A frequency-domain characterization of right poles and zeros is given in terms of a generalized frequency function