A Framework of Event-Triggered Prescribed-Time Stabilization of Time-Varying Nonlinear Systems and Its Application in Tunnel Diode Circuit

This paper investigates event-triggered prescribed-time stabilization for time-varying nonlinear systems. The motivation arises from three challenging issues: the singularity resulting from infinite control gains at the prescribed time instant, the management of infinity of implicit time variation, and trade-off between control effort and triggering intervals. Using a delicate trick that the finite value of a new time-varying function remains unchanged once all state variables of the system hit zero, we create an event-triggered strategy incorporating a sophisticated switching trigger rule equipped with a time-dependent threshold, based on the continuous feedback domination method with a series of integral functions containing nested sign functions. Better than existing results on prescribed-time stabilization, the scheme presented in this paper not only guarantees that states converge to zero precisely within the prescribed time and sustains non-truncated controller operation, but also uniquely tackles the prevention of the Zeno phenomenon. At last, the stabilization of tunnel diode circuit is conducted to confirm the validity and the effectiveness of our strategy.