Robust output regulation of linear system subject to modeled and unmodeled uncertainty

In this paper, a novel robust output regulation control framework is proposed for the system subject to noise, modeled disturbance and unmodeled disturbance to seek tracking performance and robustness simultaneously. The output regulation scheme is utilized in the framework to track the reference in the presence of modeled disturbance, and the effect of unmodeled disturbance is reduced by an $\mathcal{H}_\infty$ compensator. The Kalman filter can be also introduced in the stabilization loop to deal with the white noise. Furthermore, the tracking error in the presence/absence of noise and disturbance is estimated. The effectiveness and performance of our proposed control framework is verified in the numerical example by applying in the Furuta Inverted Pendulum system.