Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems

The design of a robust adaptive fuzzy observer for uncertain nonlinear dynamic systems is presented. The Lyapunov synthesis approach is used to guarantee a uniformly ultimately bounded property of the state observation error, as well as of all other signals in the closed-loop system. The realisation of the minimal dynamic order of the observer is considered. For this purpose, a method which does not need a strictly positive real condition is combined with a dynamic rule activation scheme with an online estimation of fuzzy parameters. No a priori knowledge of an upper bound on the lumped uncertainty is required. The theoretical results are illustrated through a simulation example.