A lifting approach to L2-gain analysis of periodic event-triggered and switching sampled-data control systems

W. P M H Heemels, G. E. Dullerud, A. R. Teel

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

6 Citations (Scopus)
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Abstract

In this work we are interested in the stability and L2-gain of hybrid systems with linear flow dynamics, periodic time-triggered jumps and nonlinear possibly set-valued jump maps. This class of hybrid systems includes various interesting applications such as periodic event-triggered control. In this paper we also show that sampled-data systems with arbitrarily switching controllers can be captured in this framework by requiring the jump map to be set-valued. We provide novel conditions for the internal stability and L2-gain analysis of these systems adopting a lifting-based approach. In particular, we establish that the internal stability and contractivity in terms of an L2-gain smaller than 1 are equivalent to the internal stability and contractivity of a particular discrete-time set-valued nonlinear system. Despite earlier works in this direction, these novel characterisations are the first necessary and sufficient conditions for the stability and the contractivity of this class of hybrid systems. The results are illustrated through multiple new examples.

Original languageEnglish
Title of host publication2015 54th IEEE Conference on Decision and Control, CDC 2015, 15-18 December 2015, Osaka, Japan
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages4176-4182
Number of pages7
ISBN (Electronic)978-1-4799-7886-1
DOIs
Publication statusPublished - 8 Feb 2016
Event54th IEEE Conference on Decision and Control (CDC 2015) - "Osaka International Convention Center", Osaka, Japan
Duration: 15 Dec 201518 Dec 2015
Conference number: 54
http://www.cdc2015.ctrl.titech.ac.jp/

Conference

Conference54th IEEE Conference on Decision and Control (CDC 2015)
Abbreviated titleCDC 2015
CountryJapan
CityOsaka
Period15/12/1518/12/15
Internet address

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