Adaptive observer design for a class of Lipschitz nonlinear systems

In this paper, we investigate the problem of adaptive observer design for a class of Lipschitz nonlinear systems with parametric uncertainties in the unmeasured state dynamics. First, the convergence conditions of the nonlinear adaptive observer for a class of Lipschitz nonlinear systems are established in terms of linear matrix inequality. Then the new sufficient conditions are derived to ensure the convergence of the adaptive observer with both linear and nonlinear output correction terms. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.