{"id":"https://openalex.org/W2097458000","doi":"https://doi.org/10.1109/cdc.2007.4434803","title":"Conditions for l<inf>∞</inf> and l<inf>2</inf> system robustness for spatially invariant systems","display_name":"Conditions for l<inf>∞</inf> and l<inf>2</inf> system robustness for spatially invariant systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2097458000","doi":"https://doi.org/10.1109/cdc.2007.4434803","mag":"2097458000"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434803","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","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/A5029605592","display_name":"Azeem Sarwar","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Azeem Sarwar","raw_affiliation_strings":["Department of Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089726422","display_name":"Petros G. Voulgaris","orcid":"https://orcid.org/0000-0002-2965-3246"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Petros G. Voulgaris","raw_affiliation_strings":["Faculty of Aerospace Engineering, University of Illinois, Urbana-Champaign, USA","Illinois, University, Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Aerospace Engineering, University of Illinois, Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Illinois, University, Champaign","institution_ids":["https://openalex.org/I2801919071"]}]}],"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":0.1851014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"836","last_page":"841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.998199999332428,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.998199999332428,"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/T11236","display_name":"Control Systems and Identification","score":0.9962999820709229,"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":0.9921000003814697,"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/robustness","display_name":"Robustness (evolution)","score":0.8425275087356567},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6833513975143433},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39779335260391235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38141733407974243},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3527418375015259},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3466106355190277},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14378276467323303},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.1232907772064209},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11902517080307007},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.11522781848907471},{"id":"https://openalex.org/keywords/biochemistry","display_name":"Biochemistry","score":0.061248779296875},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.05634787678718567}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8425275087356567},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6833513975143433},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39779335260391235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38141733407974243},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3527418375015259},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3466106355190277},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14378276467323303},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1232907772064209},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11902517080307007},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.11522781848907471},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.061248779296875},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.05634787678718567}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434803","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1970868548","https://openalex.org/W2106988738","https://openalex.org/W2119873815","https://openalex.org/W2120627201","https://openalex.org/W2138689084","https://openalex.org/W2565145308"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"We":[0],"consider":[1,19],"spatiotemporal":[2,14],"systems":[3],"and":[4,24,27,40,44,68,74],"study":[5],"their":[6],"l\u221eand":[7],"l2robustness":[8],"properties":[9],"in":[10],"the":[11,34,55,72],"presence":[12],"of":[13],"perturbations.":[15,89],"In":[16],"particular,":[17],"we":[18],"spatially":[20,41],"invariant":[21,82],"nominal":[22],"models":[23,83],"provide":[25],"necessary":[26],"sufficient":[28],"conditions":[29,51],"for":[30,71,78],"system":[31],"robustness":[32],"when":[33],"underlying":[35],"perturbations":[36],"are":[37,52],"linear":[38,80,86],"time":[39,81,87],"varying,":[42],"unstructured":[43],"structured.":[45],"It":[46],"turns":[47],"out":[48],"that":[49],"these":[50],"analogous":[53],"to":[54,63,85],"scaled":[56],"small":[57],"gain":[58],"condition":[59,67],"(which":[60],"is":[61],"equivalent":[62],"a":[64],"spectral":[65],"radius":[66],"an":[69],"LMI":[70],"l\u221e":[73],"l2case":[75],"respectively)":[76],"derived":[77],"standard":[79],"subject":[84],"varying":[88]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}