Stability of truncated sampled-data control systems with impulsive effects

This article considers the stability problem of truncated sampled-data control systems with impulsive effects. We propose the concept of average sampling interval (ASI), in which the constraint on the lower/upper bound of sampling intervals is removed to handle the sampling intervals from the holistic perspective. Then, in the framework of the input delay method, we transform the addressed system into an equivalent switched time-delay system subject to the impulsive effects that result from the truncated sampled-data control law. Interestingly, it is shown that the truncation of the sampled-data control input, which is an extension of the classical zero-order hold function, can play a stabilizing role in the presence of impulsive effects. Next, based on the ASI concept, the idea of average truncated length is introduced and the corresponding relaxed stability criteria are derived for the truncated sampled-data control systems. Particularly, the potential destabilizing impact of impulsive effects on the stability is theoretically revealed. It is also shown that under certain conditions, a truncated sampled-data system can remain stable if the magnitude of the impulsive effects is sufficiently small. Finally, two illustrative examples are presented to show the validity and also the advantages of the obtained results.