{"id":"https://openalex.org/W2086973791","doi":"https://doi.org/10.1109/cdc.2011.6160916","title":"A scaling and squaring method for the discretisation of positive switched systems","display_name":"A scaling and squaring method for the discretisation of positive switched systems","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2086973791","doi":"https://doi.org/10.1109/cdc.2011.6160916","mag":"2086973791"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160916","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055254087","display_name":"Annalisa Zappavigna","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"A. Zappavigna","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Milano, Italy","Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Milano, Italy","institution_ids":[]},{"raw_affiliation_string":"Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067595796","display_name":"Patrizio Colaneri","orcid":"https://orcid.org/0000-0002-6465-0737"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"P. Colaneri","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Milano, Italy","Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Milano, Italy","institution_ids":[]},{"raw_affiliation_string":"Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058163539","display_name":"Steve Kirkland","orcid":"https://orcid.org/0000-0002-9496-5553"},"institutions":[{"id":"https://openalex.org/I157286207","display_name":"National University of Ireland, Maynooth","ror":"https://ror.org/048nfjm95","country_code":"IE","type":"education","lineage":["https://openalex.org/I157286207"]},{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IE","IT"],"is_corresponding":false,"raw_author_name":"S. Kirkland","raw_affiliation_strings":["Hamilton Institute, National University of Ireland, Maynooth, Ireland","Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy"],"affiliations":[{"raw_affiliation_string":"Hamilton Institute, National University of Ireland, Maynooth, Ireland","institution_ids":["https://openalex.org/I157286207"]},{"raw_affiliation_string":"Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036373073","display_name":"Robert Shorten","orcid":"https://orcid.org/0000-0002-9239-2499"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]},{"id":"https://openalex.org/I157286207","display_name":"National University of Ireland, Maynooth","ror":"https://ror.org/048nfjm95","country_code":"IE","type":"education","lineage":["https://openalex.org/I157286207"]}],"countries":["IE","IT"],"is_corresponding":false,"raw_author_name":"R. Shorten","raw_affiliation_strings":["Hamilton Institute, National University of Ireland, Maynooth, Ireland","Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy"],"affiliations":[{"raw_affiliation_string":"Hamilton Institute, National University of Ireland, Maynooth, Ireland","institution_ids":["https://openalex.org/I157286207"]},{"raw_affiliation_string":"Politecnico di Milano - Dipartimento di Elettronica e Informazione, Via Ponzio 34/5 - 20133, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055254087"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14316362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":null,"first_page":"4084","last_page":"4089"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.9135716557502747},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7047907114028931},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6135678291320801},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.582720160484314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5735822916030884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5259100198745728},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5228279829025269},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5115112066268921},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5041290521621704},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4940410256385803},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43148335814476013},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.42299383878707886},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39388036727905273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3644735515117645},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23765143752098083},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0705048143863678},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.054824650287628174}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.9135716557502747},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7047907114028931},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6135678291320801},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.582720160484314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5735822916030884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5259100198745728},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5228279829025269},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5115112066268921},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5041290521621704},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4940410256385803},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43148335814476013},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.42299383878707886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39388036727905273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3644735515117645},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23765143752098083},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0705048143863678},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.054824650287628174},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160916","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W395919981","https://openalex.org/W589682677","https://openalex.org/W1500921805","https://openalex.org/W1546246264","https://openalex.org/W1552094772","https://openalex.org/W1576664335","https://openalex.org/W1646650272","https://openalex.org/W2003732027","https://openalex.org/W2028739770","https://openalex.org/W2071878037","https://openalex.org/W2089268004","https://openalex.org/W2132210216","https://openalex.org/W2136491310","https://openalex.org/W2139707868","https://openalex.org/W2158118170","https://openalex.org/W2165320992","https://openalex.org/W2498647973","https://openalex.org/W2586141080","https://openalex.org/W2798909945","https://openalex.org/W4235143360","https://openalex.org/W4295016751","https://openalex.org/W4299687166"],"related_works":["https://openalex.org/W2220253973","https://openalex.org/W1905581482","https://openalex.org/W2991666192","https://openalex.org/W2000898041","https://openalex.org/W2131032422","https://openalex.org/W3186957793","https://openalex.org/W2186188480","https://openalex.org/W2968514504","https://openalex.org/W2372280177","https://openalex.org/W3203676140"],"abstract_inverted_index":{"In":[0,26],"this":[1],"paper":[2],"we":[3],"present":[4],"a":[5,14],"new":[6],"method":[7,18,29,60],"for":[8,49],"approximating":[9],"the":[10,28,37,53,59,67],"matrix":[11],"exponential":[12],"of":[13,36,46,58,66,69],"Metzler":[15],"matrix.":[16],"This":[17],"is":[19,61],"useful":[20],"in":[21,52],"discretising":[22],"switched":[23],"positive":[24,54,75],"systems.":[25,77],"particular,":[27],"preserves":[30],"both":[31],"linear":[32,76],"and":[33],"quadratic":[34],"stability":[35],"original":[38],"continuous":[39],"time":[40],"system,":[41],"as":[42,44],"well":[43],"positivity":[45],"states":[47],"starting":[48],"initial":[50],"conditions":[51],"orthant.":[55],"The":[56],"usefulness":[57],"highlighted":[62],"by":[63],"illustrating":[64],"some":[65],"drawbacks":[68],"Pad\u00e9":[70],"approximations":[71],"when":[72],"applied":[73],"to":[74]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}