Algebraic Properties of Transfer Function Matrices for Meromorphic Nonlinear Time-Varying Systems

Abstract

We define, in terms of noncommutative algebra, a transfer function matrix of a meromorphic nonlinear time-varying system, which algebraically characterizes the input-output relation of the system. Although the transfer function matrix represents the input-output relation of the system, the matrix derived from the state-space representation can depend on the state variables. By exploiting the results of noncommutative algebra, it is shown that the state variables can always be eliminated from the transfer function matrix.