{"id":"https://openalex.org/W2944594228","doi":"https://doi.org/10.1007/978-3-030-17344-9_13","title":"Exponential Stability for a Class of Fractional Order Dynamic Systems","display_name":"Exponential Stability for a Class of Fractional Order Dynamic Systems","publication_year":2019,"publication_date":"2019-04-17","ids":{"openalex":"https://openalex.org/W2944594228","doi":"https://doi.org/10.1007/978-3-030-17344-9_13","mag":"2944594228"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-17344-9_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-17344-9_13","pdf_url":null,"source":{"id":"https://openalex.org/S4210179954","display_name":"Lecture notes in electrical engineering","issn_l":"1876-1100","issn":["1876-1100","1876-1119"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Electrical Engineering","raw_type":"book-chapter"},"type":"book-chapter","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/A5021309794","display_name":"Krzysztof Oprz\u0119dkiewicz","orcid":"https://orcid.org/0000-0002-8162-0011"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Oprz\u0119dkiewicz","raw_affiliation_strings":["AGH University, al. A. Mickiewicza 30, 30059, Krakow, Poland"],"raw_orcid":"https://orcid.org/0000-0002-8162-0011","affiliations":[{"raw_affiliation_string":"AGH University, al. A. Mickiewicza 30, 30059, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088180686","display_name":"Wojciech Mitkowski","orcid":"https://orcid.org/0000-0001-5704-8329"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Wojciech Mitkowski","raw_affiliation_strings":["AGH University, al. A. Mickiewicza 30, 30059, Krakow, Poland"],"raw_orcid":"https://orcid.org/0000-0001-5704-8329","affiliations":[{"raw_affiliation_string":"AGH University, al. A. Mickiewicza 30, 30059, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04936015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"174","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998000264167786,"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":0.9975000023841858,"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/mathematics","display_name":"Mathematics","score":0.7314807772636414},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6518984436988831},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5713385343551636},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5635668039321899},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5622414946556091},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5475186705589294},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5458697080612183},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5214852094650269},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5190087556838989},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4745952785015106},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46832969784736633},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4621610641479492},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.44695836305618286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3691360652446747},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29792237281799316},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12837359309196472},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12272688746452332},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08478054404258728},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08292269706726074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.059586167335510254},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05286693572998047}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7314807772636414},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6518984436988831},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5713385343551636},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5635668039321899},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5622414946556091},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5475186705589294},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5458697080612183},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5214852094650269},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5190087556838989},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4745952785015106},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46832969784736633},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4621610641479492},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.44695836305618286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3691360652446747},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29792237281799316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12837359309196472},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12272688746452332},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08478054404258728},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08292269706726074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.059586167335510254},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05286693572998047},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-17344-9_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-17344-9_13","pdf_url":null,"source":{"id":"https://openalex.org/S4210179954","display_name":"Lecture notes in electrical engineering","issn_l":"1876-1100","issn":["1876-1100","1876-1119"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Electrical Engineering","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W236966125","https://openalex.org/W331827123","https://openalex.org/W655150127","https://openalex.org/W1564897360","https://openalex.org/W2004202105","https://openalex.org/W2022692614","https://openalex.org/W2058860728","https://openalex.org/W2069284056","https://openalex.org/W2075871523","https://openalex.org/W2154761333","https://openalex.org/W2233470188","https://openalex.org/W2463271671","https://openalex.org/W2473752389","https://openalex.org/W2524309045","https://openalex.org/W2525291455","https://openalex.org/W2556784265","https://openalex.org/W2572003380","https://openalex.org/W2895788954"],"related_works":["https://openalex.org/W2135584473","https://openalex.org/W2964223869","https://openalex.org/W2626141450","https://openalex.org/W2114045837","https://openalex.org/W2792539140","https://openalex.org/W2005808740","https://openalex.org/W2295130398","https://openalex.org/W4302055909","https://openalex.org/W2082446734","https://openalex.org/W2810740133"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
