Exponential observer design for nonlinear systems with real parametric uncertainty

In this paper, we present a characterization and construction procedure of local exponential observers for nonlinear systems with real parametric uncertainty under some stability assumptions. We also show that for the classical case when the state equilibrium does not change with the disturbance, and when the plant output is purely a function of the state, there is no local asymptotic observer for the plant. Next, we show that in sharp contrast to this case, for the general case of problems where we allow the state equilibrium to change with the disturbance, there typically exist local exponential observers even when the plant output is purely a function of the state. Finally, we generalize our results for nonlinear systems with real parametric uncertainty to derive corresponding observer design results for nonlinear systems with exogenous disturbance.