Time-Varying Event-Triggered and Self-Triggered Bounded Control of Linear Systems With a Designable Minimal Interevent Time

This article establishes the linear static and dynamic time-varying event-triggered and self-triggered controllers with designable minimal interevent times (MIETs) to stabilize input constrained linear systems. We first design a static event-triggered control (ETC) algorithm, in which the control gain dependent on the solution to a parametric Lyapunov equation is time-varying and is only scheduled at a specified time decided by the static event-triggered mechanism (ETM). This can improve the control performance of the closed-loop system and save communication resources synchronously. Moreover, a dynamic ETC is designed to further increase the interevent times. Furthermore, in order to avoid the continuous monitoring of system status, the static and dynamic self-triggered control (STC) algorithms are also established. The Zeno phenomenon is avoided and the corresponding designable MIET is given in all established algorithms. Specifically, the designed control algorithms are extended to solve the corresponding semi-global stabilization problem. In some cases, the MIETs can be selected as an arbitrarily large bounded constant that has no relationship with system itself. Finally, applications to the spacecraft rendezvous control system verify the effectiveness of the designed algorithms.