Essential right inverses and system zeros

The theory of inverse dynamical systems has been and is continuing to be a keystone in the development of the theories of multivariable feedback control systems and of coding theory for reliable communication. Advances in understanding of the role of plant inverses in control system design have brought about additional insights, for example, in the general areas of decoupled design and of realistic possibilities for closed loop dynamical performance. Surprisingly enough, almost all the existing literature on inverse systems is cast in terms of matrices. Though the well known module theoretic approach to systems has been in place for a decade or more, this approach has not been fully exploited to bring out the foundations of a theory for inverse systems. This paper begins to lay such a foundation by developing a module theoretic definition of right inverse systems. One promising and immediate application of the theory is to an improved conceptual understanding of multivariable zeros.