It has been shown in previous work that asynchronous event-triggered mechanisms can reduce measurement transmissions of control systems' implementations. In this paper we study the relation between minimum bandwidth of the feedback channels and the performance of linear systems. By using the S-procedure, the parameters in an asynchronous event-triggered implementation are optimized. Threshold update delays are considered, and two methods are presented to guarantee a certain performance under such delays. With the presented results, the implementations can be tuned to reduce the amount of communication rate while guaranteeing pre-specified performance levels. Simulation results are presented illustrating the applicability of this optimal asynchronous event-triggered implementation.

Asynchronous event-triggered control (AETC) is a control strategy proposed for wireless networked implementations whose sensor nodes have limited energy supplies. Local thresholds allow the sensors to sample and to transmit local measurements independently of each other. AETC uses only one bit for each measurement transmission while still guarantees stability and predesigned performance of the closed-loop. In this paper, we extend the previous work on AETC, and study the stability and L₂-performance of periodic asynchronous event-triggered control (PAETC) for implementations with disturbances. In PAETC, the local event-triggered conditions are verified periodically at every sampling time. A dynamic controller is introduced to the PAETC framework, and the decision to transmit the controller outputs is also included in the asynchronous event-triggered mechanism to save network bandwidth. The developed theory is illustrated in a numerical example.

In networked control systems, the advent of event-triggering strategies in the sampling process has resulted in the usage reduction of network capacities, such as communication bandwidth. However, the aperiodic nature of sampling periods generated by event-triggering strategies has hindered the schedulability of such networks. In this study, we propose a framework to construct a timed safety automaton that captures the sampling behavior of perturbed LTI systems with an L₂-based triggering mechanism proposed in the literature. In this framework, the state-space is partitioned into a finite number of convex polyhedral cones, each cone representing a discrete mode in the abstracted automaton. Adopting techniques from stability analysis of retarded systems accompanied with a polytopic embedding of time, LMI conditions to characterize the sampling interval associated with each region are derived. Then, using reachability analysis, the transitions in the abstracted automaton are derived.