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The result applies to the class of structured LTI descriptor systems intrinsically associated with any linear causal bond graph. Starting from the expansion of a matrix determinant by means of the permutation group, permutation cycles are sorted and the expression is factorized. It is shown that each factor has a bond graph interpretation by means of multicycles and input\/output-multipaths. In this way, each factor is determined by the properties (gain and order) of a path-cycle family. The result is illustrated through a case study in vehicle dynamics.<\/jats:p>","DOI":"10.1177\/09596518251383203","type":"journal-article","created":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T19:18:44Z","timestamp":1763147924000},"page":"103-113","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Bond graph determination of system matrix determinant of descriptor systems"],"prefix":"10.1177","volume":"240","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-8959-7037","authenticated-orcid":false,"given":"Amine","family":"Laaribi","sequence":"first","affiliation":[{"name":"INSA Lyon, Universite Claude Bernard Lyon 1, Ecole Centrale de Lyon, CNRS, Ampere, UMR5005, Villeurbanne, France"}]},{"given":"Damien","family":"Eberard","sequence":"additional","affiliation":[{"name":"INSA Lyon, Universite Claude Bernard Lyon 1, Ecole Centrale de Lyon, CNRS, Ampere, UMR5005, Villeurbanne, France"}]},{"given":"Wilfrid","family":"Marquis-Favre","sequence":"additional","affiliation":[{"name":"INSA Lyon, Universite Claude Bernard Lyon 1, Ecole Centrale de Lyon, CNRS, Ampere, UMR5005, Villeurbanne, France"}]}],"member":"179","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(03)00104-3"},{"issue":"110229","key":"e_1_3_3_3_2","article-title":"An overview of structural systems theory","volume":"140","author":"Ramos G","year":"2022","unstructured":"Ramos G, Aguiar AP, Pequito S. 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