Finite-time stability of stochastic nonlinear systems with Markovian switching

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to...

Full description

Saved in:
Bibliographic Details
Main Authors: Juliang Yin, Xin Yu, Suiyang Khoo
Format: Conference Proceeding
Language:English
Subjects:
Differential equations
Finite-time stability
Lyapunov stability
Markov processes
Markovian switching
Mathematical model
Nonlinear systems
Stability analysis
Stochastic nonlinear systems
Switches
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 1924
container_issue
container_start_page 1919
container_title
container_volume
creator Juliang Yin
Xin Yu
Suiyang Khoo
description This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.
doi_str_mv 10.23919/ChiCC.2017.8027634
format conference_proceeding
fullrecord <record><control><sourceid>ieee_CHZPO</sourceid><recordid>TN_cdi_ieee_primary_8027634</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>8027634</ieee_id><sourcerecordid>8027634</sourcerecordid><originalsourceid>FETCH-LOGICAL-i175t-bace7c232e722f8c1bf4c1c4fcc3a5364b0e2165df446959eaccfb92ba446d503</originalsourceid><addsrcrecordid>eNotz0tOwzAYBGCDhERbOEE3vkCC346XKKKAVGAD68p2bfJD4qDYAuX2RGpXo28zmkFoS0nNuKHmru2gbWtGqK4bwrTi4gKtTdNQqbjh_BKtGFW0Yobpa7TO-YsQRQzlK_S6gwQlVAWGgHOxDnooMx7jgtF3NhfwOI2phxTshPOcSxgy_oPS4Rc7fY-_YBPOi30H6fMGXUXb53B7zg362D28t0_V_u3xub3fV0C1LJWzPmjPOAuasdh46qLw1IvoPbeSK-FIWBbLYxRCGWmC9T46w5xdfJSEb9D21AshhMPPBIOd5sP5O_8HvoxQng</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype></control><display><type>conference_proceeding</type><title>Finite-time stability of stochastic nonlinear systems with Markovian switching</title><source>IEEE Xplore All Conference Series</source><creator>Juliang Yin ; Xin Yu ; Suiyang Khoo</creator><creatorcontrib>Juliang Yin ; Xin Yu ; Suiyang Khoo</creatorcontrib><description>This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.</description><identifier>EISSN: 2161-2927</identifier><identifier>EISBN: 9881563933</identifier><identifier>EISBN: 9789881563934</identifier><identifier>DOI: 10.23919/ChiCC.2017.8027634</identifier><language>eng</language><publisher>Technical Committee on Control Theory, CAA</publisher><subject>Differential equations ; Finite-time stability ; Lyapunov stability ; Markov processes ; Markovian switching ; Mathematical model ; Nonlinear systems ; Stability analysis ; Stochastic nonlinear systems ; Switches</subject><ispartof>2017 36th Chinese Control Conference (CCC), 2017, p.1919-1924</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8027634$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,780,784,789,790,23930,23931,25140,27925,54555,54932</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/8027634$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Juliang Yin</creatorcontrib><creatorcontrib>Xin Yu</creatorcontrib><creatorcontrib>Suiyang Khoo</creatorcontrib><title>Finite-time stability of stochastic nonlinear systems with Markovian switching</title><title>2017 36th Chinese Control Conference (CCC)</title><addtitle>ChiCC</addtitle><description>This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.</description><subject>Differential equations</subject><subject>Finite-time stability</subject><subject>Lyapunov stability</subject><subject>Markov processes</subject><subject>Markovian switching</subject><subject>Mathematical model</subject><subject>Nonlinear systems</subject><subject>Stability analysis</subject><subject>Stochastic nonlinear systems</subject><subject>Switches</subject><issn>2161-2927</issn><isbn>9881563933</isbn><isbn>9789881563934</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2017</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><recordid>eNotz0tOwzAYBGCDhERbOEE3vkCC346XKKKAVGAD68p2bfJD4qDYAuX2RGpXo28zmkFoS0nNuKHmru2gbWtGqK4bwrTi4gKtTdNQqbjh_BKtGFW0Yobpa7TO-YsQRQzlK_S6gwQlVAWGgHOxDnooMx7jgtF3NhfwOI2phxTshPOcSxgy_oPS4Rc7fY-_YBPOi30H6fMGXUXb53B7zg362D28t0_V_u3xub3fV0C1LJWzPmjPOAuasdh46qLw1IvoPbeSK-FIWBbLYxRCGWmC9T46w5xdfJSEb9D21AshhMPPBIOd5sP5O_8HvoxQng</recordid><startdate>201707</startdate><enddate>201707</enddate><creator>Juliang Yin</creator><creator>Xin Yu</creator><creator>Suiyang Khoo</creator><general>Technical Committee on Control Theory, CAA</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>201707</creationdate><title>Finite-time stability of stochastic nonlinear systems with Markovian switching</title><author>Juliang Yin ; Xin Yu ; Suiyang Khoo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i175t-bace7c232e722f8c1bf4c1c4fcc3a5364b0e2165df446959eaccfb92ba446d503</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Differential equations</topic><topic>Finite-time stability</topic><topic>Lyapunov stability</topic><topic>Markov processes</topic><topic>Markovian switching</topic><topic>Mathematical model</topic><topic>Nonlinear systems</topic><topic>Stability analysis</topic><topic>Stochastic nonlinear systems</topic><topic>Switches</topic><toplevel>online_resources</toplevel><creatorcontrib>Juliang Yin</creatorcontrib><creatorcontrib>Xin Yu</creatorcontrib><creatorcontrib>Suiyang Khoo</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE/IET Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Juliang Yin</au><au>Xin Yu</au><au>Suiyang Khoo</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Finite-time stability of stochastic nonlinear systems with Markovian switching</atitle><btitle>2017 36th Chinese Control Conference (CCC)</btitle><stitle>ChiCC</stitle><date>2017-07</date><risdate>2017</risdate><spage>1919</spage><epage>1924</epage><pages>1919-1924</pages><eissn>2161-2927</eissn><eisbn>9881563933</eisbn><eisbn>9789881563934</eisbn><abstract>This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.</abstract><pub>Technical Committee on Control Theory, CAA</pub><doi>10.23919/ChiCC.2017.8027634</doi><tpages>6</tpages></addata></record>
fulltext fulltext_linktorsrc
identifier EISSN: 2161-2927
ispartof 2017 36th Chinese Control Conference (CCC), 2017, p.1919-1924
issn 2161-2927
language eng
recordid cdi_ieee_primary_8027634
source IEEE Xplore All Conference Series
subjects Differential equations
Finite-time stability
Lyapunov stability
Markov processes
Markovian switching
Mathematical model
Nonlinear systems
Stability analysis
Stochastic nonlinear systems
Switches
title Finite-time stability of stochastic nonlinear systems with Markovian switching
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T06%3A45%3A48IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ieee_CHZPO&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=proceeding&rft.atitle=Finite-time%20stability%20of%20stochastic%20nonlinear%20systems%20with%20Markovian%20switching&rft.btitle=2017%2036th%20Chinese%20Control%20Conference%20(CCC)&rft.au=Juliang%20Yin&rft.date=2017-07&rft.spage=1919&rft.epage=1924&rft.pages=1919-1924&rft.eissn=2161-2927&rft_id=info:doi/10.23919/ChiCC.2017.8027634&rft.eisbn=9881563933&rft.eisbn_list=9789881563934&rft_dat=%3Cieee_CHZPO%3E8027634%3C/ieee_CHZPO%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-i175t-bace7c232e722f8c1bf4c1c4fcc3a5364b0e2165df446959eaccfb92ba446d503%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_ieee_id=8027634&rfr_iscdi=true