{"id":"https://openalex.org/W2901424521","doi":"https://doi.org/10.1109/iceee.2018.8533987","title":"State-Space Formulas for Anisotropic Norm of Linear Discrete Time Varying Stochastic System","display_name":"State-Space Formulas for Anisotropic Norm of Linear Discrete Time Varying Stochastic System","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2901424521","doi":"https://doi.org/10.1109/iceee.2018.8533987","mag":"2901424521"},"language":"en","primary_location":{"id":"doi:10.1109/iceee.2018.8533987","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iceee.2018.8533987","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)","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/A5051134447","display_name":"Arkadiy Yu. Kustov","orcid":"https://orcid.org/0000-0003-2524-8654"},"institutions":[{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Arkadiy Yu. Kustov","raw_affiliation_strings":["Institute of Control Sciences, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Control Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051134447"],"corresponding_institution_ids":["https://openalex.org/I4210157430"],"apc_list":null,"apc_paid":null,"fwci":1.6823,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.85426338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"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":0.9990000128746033,"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":0.9990000128746033,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T13983","display_name":"Cybersecurity and Information Systems","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6299953460693359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6221539974212646},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5591558218002319},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5218964219093323},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49342551827430725},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4929816722869873},{"id":"https://openalex.org/keywords/discrete-time-stochastic-process","display_name":"Discrete-time stochastic process","score":0.4877625107765198},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4780229330062866},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.468448668718338},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4558171331882477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4037877321243286},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.29105979204177856},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.2566274404525757},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2292328178882599},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1350829005241394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10814112424850464}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6299953460693359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6221539974212646},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5591558218002319},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5218964219093323},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49342551827430725},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4929816722869873},{"id":"https://openalex.org/C92703954","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Discrete-time stochastic process","level":4,"score":0.4877625107765198},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4780229330062866},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.468448668718338},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4558171331882477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4037877321243286},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.29105979204177856},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.2566274404525757},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2292328178882599},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1350829005241394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10814112424850464},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iceee.2018.8533987","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iceee.2018.8533987","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)","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":27,"referenced_works":["https://openalex.org/W130083205","https://openalex.org/W1594099726","https://openalex.org/W1868559974","https://openalex.org/W1968315580","https://openalex.org/W1988668417","https://openalex.org/W2018295752","https://openalex.org/W2039873336","https://openalex.org/W2042106612","https://openalex.org/W2043880592","https://openalex.org/W2047993072","https://openalex.org/W2059706201","https://openalex.org/W2065313971","https://openalex.org/W2090167557","https://openalex.org/W2094070726","https://openalex.org/W2100827217","https://openalex.org/W2105201114","https://openalex.org/W2114423474","https://openalex.org/W2159945402","https://openalex.org/W2464638372","https://openalex.org/W2623785075","https://openalex.org/W2731637442","https://openalex.org/W3019559503","https://openalex.org/W4249925951","https://openalex.org/W4285719527","https://openalex.org/W6719652682","https://openalex.org/W6776393423","https://openalex.org/W6922411262"],"related_works":["https://openalex.org/W2022292713","https://openalex.org/W2912324827","https://openalex.org/W2171105877","https://openalex.org/W2789985026","https://openalex.org/W2913519323","https://openalex.org/W1603461487","https://openalex.org/W3123169305","https://openalex.org/W2098954817","https://openalex.org/W2477147293","https://openalex.org/W4238487991"],"abstract_inverted_index":{"In":[0,35],"this":[1,38],"paper,":[2],"the":[3,27,40,51,64],"problem":[4,29],"of":[5,7,10,44,50,53,56],"computation":[6],"anisotropic":[8],"norm":[9],"linear":[11],"discrete":[12],"time":[13],"varying":[14],"finite":[15],"horizon":[16],"stochastic":[17,67],"system":[18,58],"in":[19,30],"state-space":[20],"terms":[21],"is":[22,33],"solved.":[23],"The":[24],"relationship":[25],"with":[26,63],"similar":[28],"deterministic":[31],"setting":[32],"given.":[34],"contrary":[36],"to":[37],"case,":[39],"obtained":[41],"formulas":[42],"consist":[43],"one":[45],"more":[46],"matrix":[47],"equation":[48],"because":[49],"decomposition":[52],"random":[54],"matrices":[55],"a":[57],"into":[59],"two":[60,65],"parts":[61],"associated":[62],"first":[66],"moments.":[68]},"counts_by_year":[{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-17T06:59:57.516163","created_date":"2025-10-10T00:00:00"}