Almost Global Finite-time Stability of Invariant Sets

Research output: Contribution to conference without publisher/journalPaper without publisher/journalResearchpeer-review

Abstract

A relation between finite-time stability and Rantzer's density function has been presented for both discrete- and continuous-time system. We show that the existence of an integrable Rantzer function (also called Lyapunov density or Lyapunov measure) implies the convergence of almost all trajectories to an invariant set in finite time. The proofs utilise the duality between Frobenious-Perron operator and Koopman operator, as well as Rantzer's lemma for the evolution of densities. To illustrate the theoretical results, some illustrative examples are presented. Additionally, a transformation that removes the integrability assumption has been addressed which makes the problem of the construction of a Rantzer function numerically tractable.
Original languageEnglish
Publication date2018
Publication statusPublished - 2018
Event57th IEEE Conference on Decision and Control - Florida, United States
Duration: 17 Dec 201819 Dec 2018
https://cdc2018.ieeecss.org/index.php

Conference

Conference57th IEEE Conference on Decision and Control
CountryUnited States
CityFlorida
Period17/12/201819/12/2018
Internet address

Fingerprint

Finite-time Stability
Invariant Set
Global Stability
Lyapunov
Continuous-time Systems
Discrete-time Systems
Operator
Density Function
Integrability
Lemma
Duality
Trajectory
Imply

Cite this

Karabacak, Ö., Wisniewski, R., & Kivilcim, A. (2018). Almost Global Finite-time Stability of Invariant Sets. Paper presented at 57th IEEE Conference on Decision and Control, Florida, United States.
Karabacak, Özkan ; Wisniewski, Rafal ; Kivilcim, Aysegul. / Almost Global Finite-time Stability of Invariant Sets. Paper presented at 57th IEEE Conference on Decision and Control, Florida, United States.
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Karabacak, Ö, Wisniewski, R & Kivilcim, A 2018, 'Almost Global Finite-time Stability of Invariant Sets' Paper presented at, Florida, United States, 17/12/2018 - 19/12/2018, .

Almost Global Finite-time Stability of Invariant Sets. / Karabacak, Özkan; Wisniewski, Rafal; Kivilcim, Aysegul.

2018. Paper presented at 57th IEEE Conference on Decision and Control, Florida, United States.

Research output: Contribution to conference without publisher/journalPaper without publisher/journalResearchpeer-review

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T1 - Almost Global Finite-time Stability of Invariant Sets

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AU - Wisniewski, Rafal

AU - Kivilcim, Aysegul

PY - 2018

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N2 - A relation between finite-time stability and Rantzer's density function has been presented for both discrete- and continuous-time system. We show that the existence of an integrable Rantzer function (also called Lyapunov density or Lyapunov measure) implies the convergence of almost all trajectories to an invariant set in finite time. The proofs utilise the duality between Frobenious-Perron operator and Koopman operator, as well as Rantzer's lemma for the evolution of densities. To illustrate the theoretical results, some illustrative examples are presented. Additionally, a transformation that removes the integrability assumption has been addressed which makes the problem of the construction of a Rantzer function numerically tractable.

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Karabacak Ö, Wisniewski R, Kivilcim A. Almost Global Finite-time Stability of Invariant Sets. 2018. Paper presented at 57th IEEE Conference on Decision and Control, Florida, United States.