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In networked control systems, the advent of event-triggering strategies inthe sampling process has resulted in the usage reduction of network capacities,such as communication bandwidth. However, the aperiodic nature of samplingperiods generated by event-triggering strategies has hindered theschedulability of such networks. In this study, we propose a framework toconstruct a timed safety automaton that captures the sampling behavior ofperturbed LTI systems with an $\mathcal{L}_2$-based triggering mechanismsproposed in the Literature. In this framework, the state-space is partitionedinto a finite number of convex polyhedral cones, each cone representing adiscrete mode in the abstracted automaton. Adopting techniques from stabilityanalysis of retarded systems accompanied with a polytopic embedding of time,LMI conditions to characterize the sampling interval associated with eachregion are derived. Then, using reachability analysis, the transitions in theabstracted automaton are derived.

Technical Report: Timing Abstraction of Perturbed LTI systems with $\mathcal{L}_2$-based Event-Triggering Mechanism