Event‐Based Ultimately Bounded Observer Design for a Class of Nonlinear Systems With Periodic Disturbances: An Iterative Learning Approach

ABSTRACT In this paper, the observer design problem is investigated for a class of nonlinear systems with periodic disturbances. An iterative learning observer (ILO) is constructed to handle the periodic disturbances. Within this ILO, a variable is employed to estimate the periodic disturbances using the iterative learning technique, thereby ensuring satisfactory accuracy in state estimation. To conserve communication resources, an event‐triggered mechanism is utilized to determine the release of measurements to the ILO. The objective of this paper is to design the ILO such that the estimation error system is exponentially ultimately bounded, with the ultimate bound ensured to be independent of the periodic disturbances. First, sufficient conditions are provided to guarantee the ultimate boundedness of the estimation error system. Then, the ILO gains are computed by solving certain linear matrix inequalities. Finally, the effectiveness of the proposed ILO design scheme is validated through a simulation example.