Observer-based robust adaptive fuzzy control of uncertain nonlinear systems with delayed output

In this paper, an observer-based robust adaptive fuzzy controller is proposed to deal with the output tracking control problem for a class of uncertain single-input single-output (SISO) nonlinear systems with output delay and unmatched uncertainties.Within this scheme, the state observer is applied for estimating all states which are not available for measurement in the system, and then fuzzy logic systems and some adaptive laws are used to approximate the unknown nonlinear functions and the unknown upper bounds of unmatched uncertainties. By constructing an appropriate Lyapunov function and solving Lyapunov equations, the proposed robust adaptive fuzzy controller can guarantee that the asymptotic stabilization and the output tracking performance of the whole closed-loop system can be achieved. Finally, an example is given to illustrate the effectiveness of the proposed approach.