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

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.