Asymptotic behavior of inter-event times in planar systems under event-triggered control

Rajan, A and Tallapragada, P (2024) Asymptotic behavior of inter-event times in planar systems under event-triggered control. In: Nonlinear Analysis: Hybrid Systems, 53 .

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Abstract

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of the �angle� of the state at an event. This viewpoint allows us to analyze the inter-event times by studying the fixed points of the angle map, which represents the evolution of the �angle� of the state from one event to the next. We provide a sufficient condition for the convergence or non-convergence of inter-event times to a steady state value under a scale-invariant event-triggering rule. Following up on this, we further analyze the inter-event time behavior in the special case of threshold based event-triggering rule and we provide various conditions for convergence or non-convergence of inter-event times to a constant. We also analyze the asymptotic average inter-event time as a function of the angle of the initial state of the system. With the help of ergodic theory, we provide a sufficient condition for the asymptotic average inter-event time to be a constant for all non-zero initial states of the system. Then, we consider a special case where the angle map is an orientation-preserving homeomorphism. Using rotation theory, we comment on the asymptotic behavior of the inter-event times, including on whether the inter-event times converge to a periodic sequence. We illustrate the proposed results through numerical simulations. © 2024 Elsevier Ltd

Item Type:	Journal Article
Publication:	Nonlinear Analysis: Hybrid Systems
Publisher:	Elsevier Ltd
Additional Information:	The copyright for this article belongs to authors.
Keywords:	Asymptotic analysis; Linear systems, Asymptotic behaviour; Asymptotics; Condition; Event-triggered controls; Events triggering; General class; Inter-event time; Paper analysis; Planar systems; Scale-invariant, Networked control systems
Department/Centre:	Division of Electrical Sciences > Electrical Engineering Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems
Date Deposited:	08 Jul 2024 06:24
Last Modified:	08 Jul 2024 06:24
URI:	http://eprints.iisc.ac.in/id/eprint/84735

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