Robust Observer for Linear Impulsive Switched Systems in the Presence of Unknown Input Signal and Measurement Noise

This study presents a robust state estimator for linear impulsive switched systems subject to unknown input signals and measurement noise. Such systems exhibit highly complex behaviour due to sudden dynamic changes and external disturbances, which significantly complicates the state estimation process. The presence of unknown inputs and measurement noise may not only degrade estimation accuracy but also challenge the stability of conventional observers. To overcome these difficulties, a novel full-order observer design is proposed that does not require output differentiation, thereby eliminating impulsive effects typically caused by differentiating noisy outputs. Moreover, the proposed framework explicitly accounts for measurement noise, an aspect that has rarely been addressed in the context of impulsive or switched systems. The proposed estimator ensures exponential convergence of estimation errors while simultaneously enhancing accuracy and robustness under impulsive switching conditions. The effectiveness of the method is demonstrated through simulations on an electrical circuit with variable loads. The results confirm that accurate and stable state estimation is achieved even under fast switching and in the presence of disturbances, thereby highlighting the practical applicability of the proposed approach.