Adaptive Fuzzy Observer for Uncertain Nonlinear Systems

In this paper, one presents a unified adaptive fuzzy observer design framework for a class of uncertain nonlinear systems. The corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used high-gain (HG)-based observers, namely the usual HG observers and the sliding mode observers together with their implementable versions. Without resorting to the strictly positive real condition or the filtering of the observation error, a proportional-integral law for updating the fuzzy parameters is proposed. The proportional part is used to deal with the fuzzy approximation errors and the external disturbances. Ultimately boundedness of the error signals in the closed-loop system is shown through Lyapunov's direct method.