A brief survey on dynamical systems with saturated impulses

In this paper, the research results on dynamical systems with saturated impulses (DSSI) are reviewed. We emphasize on the fundamental results, and the recent progress of the saturated impulse theories and the typical applications. Four aspects of saturated impulse are surveyed. That is, the common DSSI models with the important definitions and lemmas, the basic ideas for dealing with the saturated impulses, the estimation of the domain of attraction (DOA) for DSSI, and the typical applications of DSSI. The typical applications contain the design of hybrid controller for dynamical systems, the consensus of multi-agent systems (MASs), and the stability analysis of neural networks (NNs) and other networked systems. Finally, the conclusions and some future research directions are given.