A transfer function approach to the realisation problem of nonlinear systems

Abstract

This article studies the nonlinear realisation problem, i.e. the problem of finding the state equations of a nonlinear system from the transfer function representation being easily computable from the higher order input–output differential equation. The realisation in both observer and controller canonical forms is studied. The results demonstrate a clear connection with those from linear theory. In the solution the concept of adjoint polynomials, adjoint transfer function and right factorisation of the transfer function play a key role. Finally, the results are applied for system linearisation up to input–output injection used in the observer design.