Almost Global Finite-time Stability of Invariant Sets

Publikation: Konferencebidrag uden forlag/tidsskriftPaper uden forlag/tidsskriftForskningpeer review

Resumé

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.
OriginalsprogEngelsk
Publikationsdato2018
StatusUdgivet - 2018
Begivenhed57th IEEE Conference on Decision and Control - Florida, USA
Varighed: 17 dec. 201819 dec. 2018
https://cdc2018.ieeecss.org/index.php

Konference

Konference57th IEEE Conference on Decision and Control
LandUSA
ByFlorida
Periode17/12/201819/12/2018
Internetadresse

Fingerprint

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

Citer dette

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

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

2018. Afhandling præsenteret på 57th IEEE Conference on Decision and Control, Florida, USA.

Publikation: Konferencebidrag uden forlag/tidsskriftPaper uden forlag/tidsskriftForskningpeer review

TY - CONF

T1 - Almost Global Finite-time Stability of Invariant Sets

AU - Karabacak, Özkan

AU - Wisniewski, Rafal

AU - Kivilcim, Aysegul

PY - 2018

Y1 - 2018

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.

AB - 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. Afhandling præsenteret på 57th IEEE Conference on Decision and Control, Florida, USA.