Full‐order impulsive observers for impulsive systems with unknown inputs

Abstract

AbstractThis paper studies full‐order impulsive observers for impulsive systems with unknown inputs. Two types of full‐order impulsive observers are designed respectively. The first type is Luenberger‐type impulsive observer (LIO). The second type is for the observed system with eliminable unknown input, where the impulsive observer is allowed to have nonidentical dynamic structure with the observed system. The conditions via the average dwell time technique are derived for the existence of these two types of impulsive observers. It is shown that in the LIO, the observer's state tracks the observed system's state in the sense of input‐to‐state stability (ISS). Specifically, the observer's state track completely the observed system's state if the unknown input trends to zero. While in the second type of impulsive observer, the observer's state tracks completely the observed system's state regardless of the unknown input trends to zero. Finally, three examples with simulations are presented to demonstrate the effectiveness of the theoretical results.