On dual zero spaces and inverse systems

Control system response possibilities for a finite-dimensional, linear, time-invariant plant are governed by an interaction between the possible plant transfer function inverses, when they exist, and the closed-loop response maps themselves. Possible minimal state spaces for such inverses are comprised algebraically of a space of plant zeros and a variable space of poles, with the latter having a characterization dependent upon whether the inverse is left or right. In this note, we unify the study of state spaces for left and right inverse systems by defining a dual zero space. The dualization is natural and extends to both the state space and the variable pole space.