Adaptive observer for a large class of nonlinear systems with exponential convergence of parameter estimation

This paper investigates the design of an adaptive observer for a large class of nonlinear systems with linearly dependent parameters that are jointed with unmeasured regression dynamics. An exponential stability of both the state and parameter errors is developed under the persistent excitation (PE) condition. The calculus of the observer gain and the adaptation law parameters is cast as a linear matrix inequality (LMI) feasibility problem. A simulation example is shown to demonstrate the effectiveness of the theoretical design.