Lyapunov Stability of Differential Inclusions Involving Prox-Regular Sets via Maximal Monotone Operators
Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed...
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| Autor*in: |
Adly, Samir [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Systematik: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of optimization theory and applications - Springer US, 1967, 182(2018), 3 vom: 23. Nov., Seite 906-934 |
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| Übergeordnetes Werk: |
volume:182 ; year:2018 ; number:3 ; day:23 ; month:11 ; pages:906-934 |
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| DOI / URN: |
10.1007/s10957-018-1446-7 |
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| 520 | |a Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions. | ||
| 650 | 4 | |a Differential inclusions | |
| 650 | 4 | |a Prox-regular sets | |
| 650 | 4 | |a Maximal monotone operators | |
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| 650 | 4 | |a Invariant sets | |
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| 700 | 1 | |a Hantoute, Abderrahim |0 (orcid)0000-0002-7347-048X |4 aut | |
| 700 | 1 | |a Nguyen, Bao Tran |4 aut | |
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10.1007/s10957-018-1446-7 doi (DE-627)OLC2026507503 (DE-He213)s10957-018-1446-7-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Adly, Samir verfasserin aut Lyapunov Stability of Differential Inclusions Involving Prox-Regular Sets via Maximal Monotone Operators 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions. Differential inclusions Prox-regular sets Maximal monotone operators Lyapunov functions -Lyapunov pairs Invariant sets Observer designs Hantoute, Abderrahim (orcid)0000-0002-7347-048X aut Nguyen, Bao Tran aut Enthalten in Journal of optimization theory and applications Springer US, 1967 182(2018), 3 vom: 23. Nov., Seite 906-934 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:182 year:2018 number:3 day:23 month:11 pages:906-934 https://doi.org/10.1007/s10957-018-1446-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2030 GBV_ILN_4027 GBV_ILN_4323 SA 6420 SA 6420 AR 182 2018 3 23 11 906-934 |
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10.1007/s10957-018-1446-7 doi (DE-627)OLC2026507503 (DE-He213)s10957-018-1446-7-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Adly, Samir verfasserin aut Lyapunov Stability of Differential Inclusions Involving Prox-Regular Sets via Maximal Monotone Operators 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions. Differential inclusions Prox-regular sets Maximal monotone operators Lyapunov functions -Lyapunov pairs Invariant sets Observer designs Hantoute, Abderrahim (orcid)0000-0002-7347-048X aut Nguyen, Bao Tran aut Enthalten in Journal of optimization theory and applications Springer US, 1967 182(2018), 3 vom: 23. Nov., Seite 906-934 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:182 year:2018 number:3 day:23 month:11 pages:906-934 https://doi.org/10.1007/s10957-018-1446-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2030 GBV_ILN_4027 GBV_ILN_4323 SA 6420 SA 6420 AR 182 2018 3 23 11 906-934 |
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Adly, Samir Hantoute, Abderrahim Nguyen, Bao Tran |
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Adly, Samir |
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10.1007/s10957-018-1446-7 |
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330 510 000 |
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lyapunov stability of differential inclusions involving prox-regular sets via maximal monotone operators |
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Lyapunov Stability of Differential Inclusions Involving Prox-Regular Sets via Maximal Monotone Operators |
| abstract |
Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
| abstractGer |
Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
| abstract_unstemmed |
Abstract In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more general non-smooth dynamics can be indeed remodeled into the classical theory of differential inclusions, involving maximal monotone operators. This result is new in the literature. It permits to make use of the rich and abundant achievements in the class of monotone operators to study different stability aspects, and to give new proofs for the existence, the continuity, and the differentiability of solutions. This going back and forth between these two models of differential inclusions is made possible thanks to a viability result for maximal monotone operators. Applications will concern Luenberger-like observers associated with these differential inclusions. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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| title_short |
Lyapunov Stability of Differential Inclusions Involving Prox-Regular Sets via Maximal Monotone Operators |
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