{"id":"https://openalex.org/W2569696545","doi":"https://doi.org/10.1109/cdc.2016.7798452","title":"A relaxed lyapunov condition for input-to-state stability of discrete-time nonlinear systems","display_name":"A relaxed lyapunov condition for input-to-state stability of discrete-time nonlinear systems","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2569696545","doi":"https://doi.org/10.1109/cdc.2016.7798452","mag":"2569696545"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7798452","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798452","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5009730980","display_name":"Dominic Gro\u00df","orcid":"https://orcid.org/0000-0001-8618-7600"},"institutions":[{"id":"https://openalex.org/I2799323385","display_name":"Board of the Swiss Federal Institutes of Technology","ror":"https://ror.org/01rvn4p91","country_code":"CH","type":"government","lineage":["https://openalex.org/I2799323385"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Dominic Gro\u00df","raw_affiliation_strings":["Autom. Control Lab., ETH Zurich, Zurich, Switzerland","Eidgenossische Technische Hochschule Zurich, Zurich, ZH, CH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Autom. Control Lab., ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Eidgenossische Technische Hochschule Zurich, Zurich, ZH, CH","institution_ids":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040756775","display_name":"Olaf Stursberg","orcid":"https://orcid.org/0000-0002-9600-457X"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Olaf Stursberg","raw_affiliation_strings":["Institute of Control and System Theory at the University of Kassel, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Control and System Theory at the University of Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1340","last_page":"1345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9965000152587891,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9846000075340271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7842327356338501},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7608035802841187},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7404009699821472},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.647146463394165},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.533073902130127},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5273131728172302},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.49243220686912537},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.477680504322052},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4525647461414337},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4292770326137543},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4140098989009857},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30944743752479553},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1530897617340088},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10975131392478943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07026010751724243},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05149438977241516},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.04775923490524292}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7842327356338501},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7608035802841187},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7404009699821472},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.647146463394165},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.533073902130127},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5273131728172302},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.49243220686912537},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.477680504322052},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4525647461414337},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4292770326137543},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4140098989009857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30944743752479553},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1530897617340088},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10975131392478943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07026010751724243},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05149438977241516},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.04775923490524292},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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:10.1109/cdc.2016.7798452","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798452","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","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":17,"referenced_works":["https://openalex.org/W1510122527","https://openalex.org/W1631623342","https://openalex.org/W1966614111","https://openalex.org/W1978956894","https://openalex.org/W2017493230","https://openalex.org/W2020588182","https://openalex.org/W2036826525","https://openalex.org/W2038137192","https://openalex.org/W2041454799","https://openalex.org/W2098989671","https://openalex.org/W2102737570","https://openalex.org/W2109873351","https://openalex.org/W2134078068","https://openalex.org/W2144132844","https://openalex.org/W2162053828","https://openalex.org/W2519789404","https://openalex.org/W4210417410"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W3194517843","https://openalex.org/W2534107666","https://openalex.org/W2374426356","https://openalex.org/W2121515234","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W1977987201","https://openalex.org/W1979419366"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"conditions":[3,126,129],"for":[4,26,36],"input-to-state":[5,9,27,74,138],"stability":[6,11,28,75],"(ISS)":[7],"and":[8,54],"practical":[10],"(ISpS)":[12,100],"of":[13,19,32,44,51,57,68,81,106,113,122],"nonlinear":[14],"discrete-time":[15],"systems":[16],"in":[17,38,48,65],"terms":[18],"Lyapunov":[20],"functions.":[21],"A":[22],"well":[23],"known":[24],"condition":[25,89],"is":[29,46,63,137],"the":[30,42,49,52,55,66,69,116,120,123],"existence":[31],"an":[33,61],"ISS-Lyapunov":[34,82],"function":[35],"which,":[37],"every":[39],"time":[40,94],"step,":[41],"rate":[43,56],"decrease":[45,88],"bounded":[47,64,93],"norm":[50,67],"state,":[53],"increase":[58],"due":[59],"to":[60,103],"input":[62],"input.":[70],"We":[71,118],"show":[72],"that":[73],"can":[76],"be":[77],"established":[78],"by":[79,127],"means":[80],"functions":[83],"which":[84,131],"satisfy":[85],"a":[86,92,104,109],"weaker":[87],"defined":[90],"over":[91],"interval.":[95],"Furthermore,":[96],"we":[97],"characterize":[98],"ISS":[99],"with":[101],"respect":[102],"set":[105],"states":[107],"(e.g.":[108],"consensus":[110],"subspace)":[111],"instead":[112],"only":[114],"considering":[115],"origin.":[117],"illustrated":[119],"applicability":[121],"proposed":[124],"relaxed":[125],"studying":[128],"under":[130],"suboptimal":[132],"model":[133],"predictive":[134],"control":[135],"(MPC)":[136],"stable.":[139]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
