Inverses of Linear Sequential Circuits

Abstract—This paper states the necessary and sufficient conditions for the existence of a feedforward inverse for a feedforward linear sequential circuit and gives an implicit procedure for constructing such inverses. It then goes on to give the necessary and sufficient conditions for the existence of general inverses with finite delay and gives procedures for constructing a class of such inverses. The discussion considers both the transfer function matrix description and the structural matrix description of the linear sequential circuit, together with the complementary nature of the results obtained from these two viewpoints. Finally, a large part of the work is motivated by results and techniques which have been applied in the study of continuous-time linear dynamical systems and thus serves to point out the advantages which may accrue through simultaneous study of both continuous-time systems and linear sequential circuits.