Stabilization of a class of Lipschitz Nonlinear Systems through an event-triggered impulsive controller

In this paper, the stabilization problem is addressed for a class of globally Lipschitz nonlinear dynamical systems. An event-triggered impulsive control (ETIC) method is introduced to establish asymptotic stability and exponential stability criteria for the resulting closed-loop systems without and with time delay, respectively. Compared with the extant results, a new type of switching and event-triggered impulsive systems are considered, and some general asymptotic stability and exponential stability conditions are provided. It is proved that Zeno behaviors can be excluded and the control frequency can be appropriately regulated through the appropriate selection of event parameters. Finally, an application example of the Chua&#x2019;s circuit is given to verify the efficiency of the approach and theoretical analyses. <italic>Note to Practitioners</italic>&#x2014;Since impulsive control provides an easier and cheaper strategy than continuous control, it has been widely applied to many practical situations, such as control of satellite rendezvous, synchronization of permanent magnet synchronous motors, consensus of multi-agent systems and so on. Different from the time-triggered impulsive control methods, the proposed ETIC method can flexibly regulate the control frequency, which meets the increasing requirement for reducing unnecessary waste of communication resources in modern industries. Compared with the extant results, an ETIC method is established with time-varying threshold parameters and event interval parameters in this paper. Moreover, the effects of event parameters and time delay on convergence rate are analyzed, which can provide reference for improving system performance in practical applications.