Event-triggered controllers based on the supremum norm of sampling-induced error

TL;DR

This paper introduces a new event-triggered control approach for nonlinear systems using the supremum norm of sampling-induced error, ensuring stability and Zeno-free operation.

Contribution

It presents a novel event-triggering scheme based on the input-delay method, with a contractive mapping approach for interconnected nonlinear systems.

Findings

Achieves stabilization with Zeno-free guarantees

Applicable to lower-triangular systems with uncertainties

Provides a practical event-triggering law

Abstract

The paper proposes a novel event-triggered control scheme for nonlinear systems based on the input-delay method. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, a cyclic mapping forms from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggering law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. With this idea, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.