Combined Synthesis of State Estimator and Perturbation Observer

A combined observer is synthesized by unifying the conventional linear state estimator and the perturbation observer to estimate plant uncertainties and disturbances. It enables robust state estimation for uncertain dynamical systems and simultaneously, provides full-state to the perturbation observer under output feedback conditions. The proposed combined observer is very practical since it is given as a recursive discrete-time form with minimal tuning parameters, and it requires no knowledge of the plant uncertainty. A coupled estimation error dynamics is derived, and the related technical issues such as stability and noise sensitivity are addressed. The combined observer setting is also extended to stochastic systems, and the discrete Kalman filter is reformulated by including the perturbation estimate update process. Numerical examples and experimental results validate the proposed schemes.