Impulsive natural observers for vector second‐order Lipschitz non‐linear systems.

Many mechanical systems can be modelled by vector second‐order differential equations. In this study, the observation problem of a class of vector second‐order Lipschitz non‐linear systems with discrete measurements is addressed. Under the premise that the discrete measurements of position and velocity vectors are available, an impulsive observer in the second‐order framework is designed. The proposed observation scheme ensures that the second‐order structure of the observed system can be retained, and allows the sampling on the system output to be aperiodic. The stability analysis of the observation error system is performed by employing an impulse‐time‐dependent discretised Lyapunov function based method. The novelty of the introduced Lyapunov function is that its structure relies on the partition on the impulse intervals. With the increase of the partition number, the existence condition of impulsive natural observers can be relaxed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]