GENERALIZED TRANSFER-FUNCTIONS AND INPUT-OUTPUT EQUIVALENCE

The concept of a transfer function is extended to general dynamic syst ems described by non-regular linear algebraic and integro-differential equations. The input consistency and uniqueness of the system output for the given consistent input are discussed. These two properties are closely related to the existence of a transfer function which itself does not need to be unique. Input-output equivalence in the sense that two systems have the same output for the given consistent input is pr oved to be necessary and sufficient for the existence of an input-outp ut isomorphic map between the solution spaces of the systems under zer o initial conditions.