Design of a unified adaptive fuzzy observer for uncertain nonlinear systems

This paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems. More precisely, we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high-gain or a sliding mode observer by selecting its gain appropriately. Additionally, we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances. We also show that the observation error is ultimately bounded using a Lyapunov approach without having recourse to the usual strictly positive real (SPR) condition or a suitable observation error filtering. The effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature.