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In this paper, we propose a novel nonlinear observer based on neuralnetworks, called neural observer, for observation tasks of lineartime-invariant (LTI) systems and uncertain nonlinear systems. In particular,the neural observer designed for uncertain systems is inspired by the activedisturbance rejection control, which can measure the uncertainty in real-time.The stability analysis (e.g., exponential convergence rate) of LTI anduncertain nonlinear systems (involving neural observers) are presented andguaranteed, where it is shown that the observation problems can be solved onlyusing the linear matrix inequalities (LMIs). Also, it is revealed that theobservability and controllability of the system matrices are required todemonstrate the existence of solutions of LMIs. Finally, the effectiveness ofneural observers is verified on three simulation cases, including the X-29Aaircraft model, the nonlinear pendulum, and the four-wheel steering vehicle.

Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems