# Stability and $\ell^2$-gain Analysis of Adaptive Control Systems with Event-triggered Try-once-discard Protocols

## TL;DR

This paper develops stability and $ ext{l}^2$-gain analysis methods for adaptive control systems employing event-triggered try-once-discard protocols, ensuring practical stability and performance bounds.

## Contribution

It introduces new stability conditions and $ ext{l}^2$-gain bounds for adaptive control systems with event-triggered measurement transmission protocols.

## Key findings

- Provided sufficient conditions for practical stability.
- Derived upper bounds on the $ ext{l}^2$-gain.
- Applicable to gain-scheduling and switching controllers.

## Abstract

This paper addresses the stability and $\ell^2$-gain analysis of adaptive control systems with event-triggered try-once-discard protocols. At every sampling time, an event trigger evaluates an error between the current value and the last released value of each measurement and determines whether to transmit the measurements and which measurements to transmit, based on the try-once-discard protocol and given lower and upper thresholds. For gain-scheduling controllers and switching controllers that are adaptive to the maximum error of the measurements, we obtain sufficient conditions for the practical stability and upper bounds on the $\ell^2$-gain of the closed-loop system.