How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems

This paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer (high-gain (HG) observer, sliding mode (like) observer, etc.) for a class of single-input–single-output (SISO) uncertain or ill-defined affine nonlinear systems. Indeed, the corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used HG based observers, namely for the usual HG observers and the sliding mode observers together with their implementable versions. The design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error. This particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real (SPR) condition.