Design of a joint adaptive high‐gain observer for a class of nonlinear sampled‐output system with unknown states and parameters

In this article, a joint adaptive high-gain observer design method is proposed for a class of nonlinear systems subject to sampled output data measurements. The considered class of system is characterized by a nonlinear term coupled with an unknown parameter that enters the system in both the outputs and the states equations. The fact that the considered system involves an output sampling process and an unknown parameter renders the design of the nonlinear adaptive observer more difficult. To overcome this difficulty, a novel closed-loop output predictor is proposed. Based on the well-known decoupling method between the state and unknown parameters, a joint adaptive high-gain observer which can simultaneously guarantee the exponential convergence of the estimation of the unknown state and the unknown parameter is proposed in this article. The structure of the designed observer has been extended to the case of sampled and delayed data measurements. The effectiveness of our proposed observer is demonstrated through numerical simulations and performance comparison with another observer structure proposed in the literature.