Robust state estimation for non-linear systems with unknown delays

In this study, the authors consider the state estimation problem for a class of non-linear systems with unknown time-varying delays. Based on the H∞ filtering method, they propose a new observer design approach where the states of the non-linear systems with unknown delays can be robustly estimated. While relevant results in the literature assume the unknown delays to be differentiable, the observer design proposed in this study only requires the knowledge of the unknown delays' upper and lower bounds which can be obtained in practical systems. The new observer design approach also allows us to consider delays in the output measurements. They further utilise the linear parameter varying approach to relax the conservativeness imposed on observer design conditions by the Lipschitz conditions. To show the effectiveness of the new results, the single-link joint robotic system and the pendulum system are considered as illustrative examples.