Disturbance Rejection for Nonlinear Systems Using Nonlinear-State-Observer-Based Equivalent-Input-Disturbance Approach

This article presents a nonlinear-state-observer-based equivalent-input-disturbance approach that rejects unknown exogenous disturbances while preserving intrinsic nonlinearities. First, a nonlinearity in a plant is decomposed into four parts in four subsystems based on controllability and observability. This system decomposition derives the intrinsic part of a nonlinearity. Second, the intrinsic nonlinearities are embedded in a nonlinear state observer to reconstruct. This strategy has a significant advantage because it separates intrinsic nonlinearities from disturbances. Then, a stability condition that ensures uniform ultimate boundedness for the closed-loop system is derived and gains of state feedback and observer are obtained in terms of a linear matrix inequality. After that, a method is presented to evaluate the overall effect of nonlinearity preservation and disturbance compensation. Finally, simulation results and a comparison study demonstrate the validity of the developed method and its superiority over the conventional equivalent-input- disturbance approach and the generalized extended state observer method.