Extended State Observer for Mismatch Disturbances Using Taylor Approximation of the Integral

The development of disturbance estimators using extended state observers (ESOs) typically assumes that the system is observable. This paper introduces an improved method for systems that are initially unobservable, leveraging Taylor expansion to approximate the integral of disturbance dynamics. A new extended system is formulated based on this approximation, enabling the design of an observer that achieves exponential stability of the error dynamics. The proposed method's efficacy is demonstrated through a practical example, highlighting its potential for robust disturbance estimation in dynamic systems.