{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T01:41:21Z","timestamp":1758591681258,"version":"3.44.0"},"publisher-location":"New York, NY, USA","reference-count":48,"publisher":"ACM","license":[{"start":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T00:00:00Z","timestamp":1721088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006374","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["WO 2206\/1-1"],"award-info":[{"award-number":["WO 2206\/1-1"]}],"id":[{"id":"10.13039\/501100006374","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,7,16]]},"DOI":"10.1145\/3666000.3669709","type":"proceedings-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T13:18:51Z","timestamp":1721049531000},"page":"361-370","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Initial Application of SONC to Lyapunov Stability of Dynamical Systems"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0883-1389","authenticated-orcid":false,"given":"Timo","family":"de Wolff","sequence":"first","affiliation":[{"name":"Mathematics, TU Braunschweig, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2386-8294","authenticated-orcid":false,"given":"Janin","family":"Heuer","sequence":"additional","affiliation":[{"name":"Mathematics, TU Braunschweig, Germany"}]}],"member":"320","published-online":{"date-parts":[[2024,7,16]]},"reference":[{"key":"e_1_3_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2011.6161499"},{"key":"e_1_3_2_2_2_1","unstructured":"A.A. Ahmadi and P.A. Parrilo. 2013. Stability of Polynomial Differential Equations: Complexity and Converse Lyapunov Questions. arXiv:1308.6833."},{"key":"e_1_3_2_2_3_1","doi-asserted-by":"crossref","unstructured":"G. Blekherman P.A. Parrilo and R.R. Thomas. 2013. Semidefinite Optimization and Convex Algebraic Geometry. MOS-SIAM Series on Optimization Vol.\u00a013. SIAM and the Mathematical Optimization Society Philadelphia.","DOI":"10.1137\/1.9781611972290"},{"key":"e_1_3_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/140988978"},{"key":"e_1_3_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1086303"},{"key":"e_1_3_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2018.06.018"},{"key":"e_1_3_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/21M1462568"},{"key":"e_1_3_2_2_8_1","unstructured":"P. \u00c9rdi and J. T\u00f3th. 1989. Mathematical models of chemical reactions: theory and applications of deterministic and stochastic models. Manchester University Press."},{"key":"e_1_3_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375614"},{"key":"e_1_3_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1325484"},{"key":"e_1_3_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2018049"},{"volume-title":"Stability of motion. Vol.\u00a0138","author":"W.","key":"e_1_3_2_2_12_1","unstructured":"W. Hahn 1967. Stability of motion. Vol.\u00a0138. Springer."},{"volume-title":"Ordinary differential equations","author":"Hale J.K.","key":"e_1_3_2_2_13_1","unstructured":"J.K. Hale. 2009. Ordinary differential equations. Courier Corporation."},{"key":"e_1_3_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1186\/s40687-016-0052-2"},{"key":"e_1_3_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/140962425"},{"key":"e_1_3_2_2_16_1","first-page":"1531","article-title":"Advances in computational Lyapunov analysis using sum-of-squares programming","volume":"20","year":"2015","unstructured":"A.\u00a0Papachristodoulou J.\u00a0Anderson. 2015. Advances in computational Lyapunov analysis using sum-of-squares programming. Discrete & Continuous Dynamical Systems - B 20, 1531-3492_2015_8_2361 (2015), 2361.","journal-title":"Discrete & Continuous Dynamical Systems - B"},{"volume-title":"Nonlinear Systems","author":"Khalil H.K.","key":"e_1_3_2_2_17_1","unstructured":"H.K. Khalil. 2002. Nonlinear Systems. Prentice Hall."},{"key":"e_1_3_2_2_18_1","unstructured":"J.-L. Lagrange. 1788. M\u00e9canique analytique. Vol.\u00a01. Gauthier-Villars."},{"key":"e_1_3_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623400366802"},{"volume-title":"An introduction to polynomial and semi-algebraic optimization. Vol.\u00a052","author":"Lasserre J.B.","key":"e_1_3_2_2_20_1","unstructured":"J.B. Lasserre. 2015. An introduction to polynomial and semi-algebraic optimization. Vol.\u00a052. Cambridge University Press."},{"volume-title":"Emerging Applications of Algebraic Geometry. IMA","author":"Laurent M.","key":"e_1_3_2_2_21_1","unstructured":"M. Laurent. 2009. Sums of squares, moment matrices and optimization over polynomials. In Emerging Applications of Algebraic Geometry. IMA Vol. Math. Appl., Vol.\u00a0149. Springer, New York, 157\u2013270."},{"key":"e_1_3_2_2_22_1","doi-asserted-by":"publisher","unstructured":"B. Legat T. Weisser L. Kapelevich J. Huchette A. Bhatia T. Votroubek O. Dowson M. Forets A. Moat C. Coffrin C. C. E. Saba E. Hanson G. Berger J. TagBot M. Kaluba M. Lubin S. Tu and T. Kelman. 2022. jump-dev\/SumOfSquares.jl: v0.6.2. https:\/\/doi.org\/10.5281\/zenodo.6388122","DOI":"10.5281\/zenodo.6388122"},{"key":"e_1_3_2_2_23_1","doi-asserted-by":"crossref","unstructured":"J.A.\u00a0De Loera J. Rambau and F. Santos. 2010. Triangulations. Algorithms and Computation in Mathematics Vol.\u00a025. Springer-Verlag Berlin. Structures for algorithms and applications.","DOI":"10.1007\/978-3-642-12971-1"},{"key":"e_1_3_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207179208934253"},{"key":"e_1_3_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2022.08.002"},{"key":"e_1_3_2_2_26_1","volume-title":"The Arithmetic-Geometric Inequality. In Inequalities: Proceedings","volume":"1","author":"Motzkin T.S.","year":"1967","unstructured":"T.S. Motzkin. 1967. The Arithmetic-Geometric Inequality. In Inequalities: Proceedings, Volume 1. Academic Press, 203\u2013224."},{"key":"e_1_3_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-021-09497-w"},{"key":"e_1_3_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-020-00193-4"},{"key":"e_1_3_2_2_29_1","doi-asserted-by":"crossref","unstructured":"R. Murray H. Naumann and T. Theobald. 2022. Sublinear circuits and the constrained signomial nonnegativity problem. Mathematical Programming (2022) 1\u201335.","DOI":"10.1007\/s10107-022-01776-w"},{"key":"e_1_3_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2012.17.2153"},{"key":"e_1_3_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2002.1184414"},{"key":"e_1_3_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.2514\/1.28957"},{"volume-title":"Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.\u00a0D. Dissertation","author":"Parrilo P.A.","key":"e_1_3_2_2_33_1","unstructured":"P.A. Parrilo. 2000. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.\u00a0D. Dissertation. California Institute of Technology."},{"volume-title":"Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.\u00a0D. Dissertation","author":"Parrilo P.A.","key":"e_1_3_2_2_34_1","unstructured":"P.A. Parrilo. 2000. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.\u00a0D. Dissertation. California Institute of Technology."},{"key":"e_1_3_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442738"},{"key":"e_1_3_2_2_36_1","unstructured":"J. Roskam. 1995. Airplane flight dynamics and automatic flight controls. DARcorporation."},{"volume-title":"Nonlinear systems: analysis, stability, and control","author":"Sastry S.","key":"e_1_3_2_2_37_1","unstructured":"S. Sastry. 1999. Nonlinear systems: analysis, stability, and control. Springer Science & Business Media."},{"key":"e_1_3_2_2_38_1","unstructured":"C. Schlosser and M. Korda. 2020. Sparse moment-sum-of-squares relaxations for nonlinear dynamical systems with guaranteed convergence. arXiv:2012.05572."},{"key":"e_1_3_2_2_39_1","volume-title":"POEM: Effective Methods in Polynomial Optimization, version 0.2.1.0(a)","author":"Seidler H.","year":"2019","unstructured":"H. Seidler and T. de Wolff. 2019. POEM: Effective Methods in Polynomial Optimization, version 0.2.1.0(a). http:\/\/www.iaa.tu-bs.de\/AppliedAlgebra\/POEM\/index.html."},{"key":"e_1_3_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2013.06.003"},{"key":"e_1_3_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00385-4"},{"key":"e_1_3_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2020.12.1488"},{"key":"e_1_3_2_2_43_1","unstructured":"W. Tan. 2006. Nonlinear control analysis and synthesis using sum-of-squares programming. ProQuest."},{"key":"e_1_3_2_2_44_1","doi-asserted-by":"crossref","unstructured":"M. Vidyasagar. 2002. Nonlinear systems analysis. SIAM.","DOI":"10.1137\/1.9780898719185"},{"key":"e_1_3_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1313969"},{"volume-title":"2021 American Control Conference (ACC). IEEE, 2254\u20132259","author":"Wang J.","key":"e_1_3_2_2_46_1","unstructured":"J. Wang, M. Maggio, and V. Magron. 2021. SparseJSR: A fast algorithm to compute joint spectral radius via sparse SOS decompositions. In 2021 American Control Conference (ACC). IEEE, 2254\u20132259."},{"key":"e_1_3_2_2_47_1","unstructured":"J. Wang C. Schlosser M. Korda and V. Magron. 2021. Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems. arXiv:2111.08347."},{"volume-title":"Chaos theory tamed","author":"Williams G.","key":"e_1_3_2_2_48_1","unstructured":"G. Williams. 1997. Chaos theory tamed. CRC Press."}],"event":{"name":"ISSAC '24: International Symposium on Symbolic and Algebraic Computation","sponsor":["SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"],"location":"Raleigh NC USA","acronym":"ISSAC '24"},"container-title":["Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3666000.3669709","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3666000.3669709","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T00:51:33Z","timestamp":1758588693000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3666000.3669709"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,16]]},"references-count":48,"alternative-id":["10.1145\/3666000.3669709","10.1145\/3666000"],"URL":"https:\/\/doi.org\/10.1145\/3666000.3669709","relation":{},"subject":[],"published":{"date-parts":[[2024,7,16]]},"assertion":[{"value":"2024-07-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}