mu-Stability of Positive Homogeneous Differential-Difference Equations With Unbounded Time-Varying Delays
This note studies the stability problem of nonlinear positive differential-difference equations with unbounded time-varying delays. Under assumptions on the nonlinear vector fields, such as being homogeneous, cooperative, and order-preserving, conditions are derived for positivity and asymptotic sta...
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| Veröffentlicht in: | IEEE transactions on automatic control 2024-12, Vol.69 (12), p.8852-8859 |
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| container_title | IEEE transactions on automatic control |
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| creator | Cui, Yukang Wu, Zongze Gong, Xin Basin, Michael V. Huang, Tingwen |
| description | This note studies the stability problem of nonlinear positive differential-difference equations with unbounded time-varying delays. Under assumptions on the nonlinear vector fields, such as being homogeneous, cooperative, and order-preserving, conditions are derived for positivity and asymptotic stability of nonlinear differential-difference equations, which include the corresponding linear system as a special case. This work features three main contributions: first, a necessary and sufficient positivity condition is proposed for nonlinear differential-difference equations with delays. Then, utilizing the concept of homogeneity, a necessary and sufficient condition is provided for the global asymptotic stability of such positive nonlinear systems with unbounded delays. Finally, we analyze the global \mu-stability of the systems with unbounded time-varying delays to estimate the convergence rates of the system dynamics. The effectiveness of the obtained theoretical results is illustrated by numerical examples, including an analysis of nonlinear epidemic-spreading processes. |
| doi_str_mv | 10.1109/TAC.2024.3425666 |
| format | Article |
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Under assumptions on the nonlinear vector fields, such as being homogeneous, cooperative, and order-preserving, conditions are derived for positivity and asymptotic stability of nonlinear differential-difference equations, which include the corresponding linear system as a special case. This work features three main contributions: first, a necessary and sufficient positivity condition is proposed for nonlinear differential-difference equations with delays. Then, utilizing the concept of homogeneity, a necessary and sufficient condition is provided for the global asymptotic stability of such positive nonlinear systems with unbounded delays. Finally, we analyze the global <inline-formula><tex-math notation="LaTeX">\mu</tex-math></inline-formula>-stability of the systems with unbounded time-varying delays to estimate the convergence rates of the system dynamics. The effectiveness of the obtained theoretical results is illustrated by numerical examples, including an analysis of nonlinear epidemic-spreading processes.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2024.3425666</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>IEEE</publisher><subject><![CDATA[<named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> mu</tex-math> </inline-formula> </named-content>-stability ; Asymptotic stability ; Delays ; Differential-difference equations (DDEs) ; homogeneous cooperative systems ; Mathematical models ; positive systems ; Thermal stability ; Time-varying systems ; unbounded time-varying delays ; Vectors]]></subject><ispartof>IEEE transactions on automatic control, 2024-12, Vol.69 (12), p.8852-8859</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-0597-1426 ; 0000-0002-7274-4303 ; 0000-0001-6883-5088 ; 0009-0009-8389-4276 ; 0000-0001-9610-846X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/10591356$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/10591356$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Cui, Yukang</creatorcontrib><creatorcontrib>Wu, Zongze</creatorcontrib><creatorcontrib>Gong, Xin</creatorcontrib><creatorcontrib>Basin, Michael V.</creatorcontrib><creatorcontrib>Huang, Tingwen</creatorcontrib><title>mu-Stability of Positive Homogeneous Differential-Difference Equations With Unbounded Time-Varying Delays</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>This note studies the stability problem of nonlinear positive differential-difference equations with unbounded time-varying delays. Under assumptions on the nonlinear vector fields, such as being homogeneous, cooperative, and order-preserving, conditions are derived for positivity and asymptotic stability of nonlinear differential-difference equations, which include the corresponding linear system as a special case. This work features three main contributions: first, a necessary and sufficient positivity condition is proposed for nonlinear differential-difference equations with delays. Then, utilizing the concept of homogeneity, a necessary and sufficient condition is provided for the global asymptotic stability of such positive nonlinear systems with unbounded delays. Finally, we analyze the global <inline-formula><tex-math notation="LaTeX">\mu</tex-math></inline-formula>-stability of the systems with unbounded time-varying delays to estimate the convergence rates of the system dynamics. 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Under assumptions on the nonlinear vector fields, such as being homogeneous, cooperative, and order-preserving, conditions are derived for positivity and asymptotic stability of nonlinear differential-difference equations, which include the corresponding linear system as a special case. This work features three main contributions: first, a necessary and sufficient positivity condition is proposed for nonlinear differential-difference equations with delays. Then, utilizing the concept of homogeneity, a necessary and sufficient condition is provided for the global asymptotic stability of such positive nonlinear systems with unbounded delays. Finally, we analyze the global <inline-formula><tex-math notation="LaTeX">\mu</tex-math></inline-formula>-stability of the systems with unbounded time-varying delays to estimate the convergence rates of the system dynamics. 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| subjects | <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> mu</tex-math> </inline-formula> </named-content>-stability Asymptotic stability Delays Differential-difference equations (DDEs) homogeneous cooperative systems Mathematical models positive systems Thermal stability Time-varying systems unbounded time-varying delays Vectors |
| title | mu-Stability of Positive Homogeneous Differential-Difference Equations With Unbounded Time-Varying Delays |
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