An algebra of transfer functions for distributed linear time-invariant systems

A quotient algebra of transfer functions of distributed linear time-invariant subsystems is proposed; this algebra is a generalization of the algebra of proper rational functions. Its main virtue is that it allows the algebraic manipulation of distributed systems within the algebra. Series, parallel, and, under some regularity conditions, feedback interconnection of transfer functions in the algebra remain in the algebra. The relation of our algebra to the algebras proposed by Morse, Dewilde, and Kamen is discussed and the algebras are compared. Finally, applications of the algebra are indicated.