Analysis and synthesis of minimum phase nonlinear SISO systems under external unmatched perturbations

Abstract

For the nonlinear minimum phase single-input single-output (SISO) systems, this paper formalizes the structure of the equivalent “input–output” representation taking into account the smooth perturbations that do not belong to the control space. Using this representation, we design a basic combined control law ensuring the asymptotic stability of the tracking error. In contrast to the traditional approach with generation of a reference signal and a perturbation, the complex estimation of the external signals and their derivatives employs a sliding mode observer. And finally, we formalize the physical implementability conditions of the invariant tracking system in the case when only the output (controlled variable) and the reference signal are directly measured.