Discrete-time dynamic event-triggered state observers for second-order systems and their applications to a quarter-car suspension system

This paper considers the problem of designing discrete-time dynamic event-triggered state observers for second-order systems with external disturbances. The obtained theoretical results are applied to estimate the state position and velocity vectors of a quarter-car suspension system. For the first time, state vectors of second-order systems can be robustly estimated by using a discrete-time dynamic event-triggered state observer. Unlike existing methods of designing state observers for second-order systems, which are based on Luenberger state observers, the one in this paper is a natural second-order observer. Moreover, the proposed natural second-order observer uses only information from the output vector when a discrete supervision holds. This indicates that the utilization of communication resources is reduced while maintaining the desired robust estimation performance. In addition, different from the existing method based on a parameter-dependent Lyapunov function in investigating the stability of the dynamic error system of natural second-order observers, a convex optimization problem is established in this paper to give a minimized level in evaluating the boundedness of the dynamic error system. First, a new discrete-time dynamic event-triggered natural second-order observer is designed. Then, a sufficient condition for the existence of such an observer is established. Finally, the obtained results are applied to the quarter-car suspension system.