Constructing distance functions and piecewise quadratic Lyapunov functions for stability of hybrid trajectories

J.J.B. Biemond, W.P.M.H. Heemels, R.G. Sanfelice, N. van de Wouw

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

Abstract

Characterising the distance between hybrid trajectories is crucial for solving tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. When the Euclidean distance function is used, the socalled “peaking phenomenon” for hybrid systems arises, which forms a major obstacle as trajectories cannot be stable in the sense of Lyapunov using such a distance. Therefore, in this paper, a novel and systematic way of designing appropriate distance functions is proposed that overcomes this hurdle and enables the derivation of sufficient Lyapunov-type conditions, using minimal or maximal average dwell-time arguments, for the stability of a hybrid trajectory. A constructive design method for piecewise quadratic Lyapunov functions is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. Finally, we illustrate our results with an example.
Original languageEnglish
Title of host publication54th IEEE Conference on Decision and Control (CDC 2015), 15-18 December 2015, Osaka, Japan
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages2252-2257
ISBN (Electronic)978-1-4799-7885-4
ISBN (Print)978-1-4799-7884-7
DOIs
Publication statusPublished - 2015
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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