State observer for linear system with unknown input disturbance and sampled and delayed output with measurement noise

This paper addresses the sampled and unknown time-varying delayed output problem of the continuous-time linear system with unknown input disturbance and measurement noise. Based on the piecewise continuous hybrid system and extended functional observer, a robust hybrid extended observer is proposed to estimate the non-delayed continuous state from the sampled and delayed measurements when the time delay is unknown time-varying. The advantages of the designed observer are the quite simple structure, robustness to dealing with measurement noise, and ability to estimate the system state with accuracy under the influence of unknown input disturbance. Furthermore, the proposed observer is able to estimate the non-delayed continuous state and unknown input disturbance, in particular for the issue of fault estimation and perturbation disturbance simultaneously. The stability of the robust hybrid extended observer is illustrated and analyzed. Moreover, to show the effectiveness of the proposed observer, a comparison with the delayed Luenberger observer is performed via a numerical example. Finally, the simulation results are demonstrated.