ABSTRACT
This chapter aims to study various aspects of the invertibility problem for control systems. The problem of invertibility of nonlinear control systems has also attracted a lot of attention. The chapter compares some aspects of left and right invertibility for nonlinear systems. It argues that in the linear case the existing theory is complete: one has conditions expressed in terms of the data of the system as well as others expressed in terms of its transfer matrix. There are procedures to design differential inverses and integral inverses. For linear systems everything can be easily explained in terms of the transfer matrix of the system. The state-space formulation of left and right invertibility involve the concept of initial state. If was due to Brockett and Mesarovic to given an alternative condition for the right invertibility. In studying and proving results, the chapter extensively utilizes the Extension Algorithm.
