Non-linear systems: stability and rationality

The problem of when a non-linear system can be represented as a quotient of two stable non-linear systems is considered. Attention is mainly directed toward nonlinear discrete-time recursive systems, where recursive means that the relationship between an input sequence and the corresponding output sequence can be expressed in terms of a finite number of recursive equations. Necessary and sufficient conditions are derived for the existence of a fraction representation of a recursive system, where the numerator and the denominator are stable recursive systems. The explicit construction of such a fraction representation is described.