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

TL;DR

This paper develops a framework to model the sampling behavior of perturbed LTI systems with $\\mathcal{L}_2$-based event-triggering, enabling better network resource management through timed automata abstraction.

Contribution

It introduces a novel method to construct timed automata for perturbed LTI systems with $\\mathcal{L}_2$-based triggers, combining stability analysis and reachability techniques.

Findings

Automated construction of timed automata for perturbed LTI systems.

Finite state abstraction capturing sampling behavior.

Conditions for sampling intervals derived from LMI analysis.

Abstract

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 $\mathcal{L}_2$-based triggering mechanisms 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.