Realization of discrete-time nonlinear input–output equations: Polynomial approach
The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the theory of non-commutative polynomials. First, the necessary and sufficient reducibility condition is presented in terms of the greatest common lef...
Gespeichert in:
| Veröffentlicht in: | Automatica (Oxford) Jg. 48; H. 2; S. 255 - 262 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Kidlington
Elsevier Ltd
01.02.2012
Elsevier |
| Schlagworte: | |
| ISSN: | 0005-1098, 1873-2836 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the theory of non-commutative polynomials. First, the necessary and sufficient reducibility condition is presented in terms of the greatest common left divisor of two polynomial matrices associated with the set of the higher order input–output (i/o) difference equations of the system. The condition also provides a method for system reduction, i.e. for finding the irreducible representation of the set of the i/o equations, being transfer equivalent to the original system representation. Second, to solve the realization problem, a formula is presented for computing the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The polynomial approach addressed in this paper is more direct and requires noticeably less computations than earlier methods represented in terms of subspaces of differential one-forms. |
|---|---|
| AbstractList | The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the theory of non-commutative polynomials. First, the necessary and sufficient reducibility condition is presented in terms of the greatest common left divisor of two polynomial matrices associated with the set of the higher order input–output (i/o) difference equations of the system. The condition also provides a method for system reduction, i.e. for finding the irreducible representation of the set of the i/o equations, being transfer equivalent to the original system representation. Second, to solve the realization problem, a formula is presented for computing the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The polynomial approach addressed in this paper is more direct and requires noticeably less computations than earlier methods represented in terms of subspaces of differential one-forms. |
| Author | Kotta, Ülle Tõnso, Maris |
| Author_xml | – sequence: 1 givenname: Ülle surname: KOTTA fullname: KOTTA, Ülle organization: Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia – sequence: 2 givenname: Maris surname: TONSO fullname: TONSO, Maris organization: Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=25498150$$DView record in Pascal Francis |
| BookMark | eNqNkMFqFTEUhoNU8Lb6DrMR3Mz0JHOTTFwIWtQWCkpp1yE3OYO5zCS3SUZoV76Db9gnMbe3KLjR1cmB__9O-I7JUYgBCWkodBSoON12ZilxNsVb0zGgtAPZAYVnZEUH2bds6MURWQEAbymo4QU5znlb1zUd2IpcX6GZ_H2tx9DEsXE-24QF2-JnbOqtyQc0qfFht5SHHz_jUuqjwdvlsZLfNl_jdBfi7M3UmN0uRWO_vSTPRzNlfPU0T8jNp4_XZ-ft5ZfPF2fvL1u7XsvSohqkE44KpRxjG8lBjW7DhAJ0AJYZwdBZ7F1vUCrOLFAuRruRIBSXDvoT8ubArWdvF8xFz_X7OE0mYFyyroKUYJwxXqOvn6ImWzONyQTrs94lP5t0pxlfq4HyPXI45GyKOSccf0co7HlCb_Uf4XovXIPUVXitvvuran15tFSS8dP_AD4cAFidffeYdLYeg0XnE9qiXfT_hvwCLCGoAw |
| CODEN | ATCAA9 |
| CitedBy_id | crossref_primary_10_1016_j_automatica_2015_05_007 crossref_primary_10_1016_j_ejcon_2015_01_006 crossref_primary_10_1016_j_ejcon_2013_12_004 crossref_primary_10_1049_iet_cta_2015_0765 crossref_primary_10_1109_TAC_2016_2608718 crossref_primary_10_1109_TAC_2013_2270868 crossref_primary_10_1016_j_sysconle_2015_01_006 crossref_primary_10_1016_j_ifacol_2017_08_122 crossref_primary_10_1016_j_sysconle_2013_10_009 crossref_primary_10_1080_00207179_2017_1361042 |
| Cites_doi | 10.3176/phys.math.2007.4.04 10.1109/9.964691 10.1137/S0363012994267315 10.1145/1576702.1576728 10.1109/TAC.2011.2112430 10.23919/ECC.1999.7099742 10.1137/S0363012994268412 10.23919/ECC.2009.7074700 10.1109/WCICA.2008.4592979 10.1016/j.automatica.2007.09.008 10.1109/9.920788 10.1016/S0005-1098(01)00144-3 10.1109/CDC.1998.762064 10.1076/mcmd.8.1.21.8340 10.3176/phys.math.2006.1.03 10.3182/20080706-5-KR-1001.02570 10.1007/BFb0059934 10.1016/S1474-6670(17)31232-6 10.1137/0317011 10.1080/00207170410001682506 |
| ContentType | Journal Article |
| Copyright | 2011 Elsevier Ltd 2015 INIST-CNRS |
| Copyright_xml | – notice: 2011 Elsevier Ltd – notice: 2015 INIST-CNRS |
| DBID | AAYXX CITATION IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.automatica.2011.07.010 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Applied Sciences |
| EISSN | 1873-2836 |
| EndPage | 262 |
| ExternalDocumentID | 25498150 10_1016_j_automatica_2011_07_010 S0005109811005413 |
| GrantInformation_xml | – fundername: Estonian Ministry of Education and Research grantid: SF0140018s08 – fundername: ESF grantid: 8787 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1~. 1~5 23N 3R3 4.4 457 4G. 5GY 5VS 6TJ 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABDEX ABFNM ABFRF ABJNI ABMAC ABUCO ABXDB ABYKQ ACBEA ACDAQ ACGFO ACGFS ACNNM ACRLP ADBBV ADEZE ADIYS ADMUD ADTZH AEBSH AECPX AEFWE AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHPGS AI. AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ APLSM ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HLZ HVGLF HZ~ H~9 IHE J1W JJJVA K-O KOM LG9 LY7 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ RXW SBC SDF SDG SDP SES SET SEW SPC SPCBC SSB SSD SST SSZ T5K T9H TAE TN5 VH1 WH7 WUQ X6Y XFK XPP ZMT ~G- 77I 9DU AATTM AAXKI AAYWO AAYXX ABUFD ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7SP 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c447t-e987d6d1699d22b7509fdb2690ed00c2a62edce3d3ae7952c0156fcb706957d03 |
| ISICitedReferencesCount | 26 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000301213200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0005-1098 |
| IngestDate | Mon Sep 29 06:22:51 EDT 2025 Mon Jul 21 09:14:42 EDT 2025 Tue Nov 18 22:19:00 EST 2025 Sat Nov 29 07:32:40 EST 2025 Fri Feb 23 02:14:12 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Discrete-time systems Polynomial methods Nonlinear control systems Reduction Input–output models State space realization MIMO system Polynomial matrix Reducibility System realization Necessary and sufficient condition Differential form Non linear control Polynomial equation Systems theory Polynomial method Input-output models Difference equation Non linear system Irreducible representation Discrete time System representation Input output model |
| Language | English |
| License | CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c447t-e987d6d1699d22b7509fdb2690ed00c2a62edce3d3ae7952c0156fcb706957d03 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 1019625225 |
| PQPubID | 23500 |
| PageCount | 8 |
| ParticipantIDs | proquest_miscellaneous_1019625225 pascalfrancis_primary_25498150 crossref_primary_10_1016_j_automatica_2011_07_010 crossref_citationtrail_10_1016_j_automatica_2011_07_010 elsevier_sciencedirect_doi_10_1016_j_automatica_2011_07_010 |
| PublicationCentury | 2000 |
| PublicationDate | 2012-02-01 |
| PublicationDateYYYYMMDD | 2012-02-01 |
| PublicationDate_xml | – month: 02 year: 2012 text: 2012-02-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationTitle | Automatica (Oxford) |
| PublicationYear | 2012 |
| Publisher | Elsevier Ltd Elsevier |
| Publisher_xml | – name: Elsevier Ltd – name: Elsevier |
| References | Zheng, Cao (br000150) 1995; 2 Halás, Kotta (br000040) 2009; 19 Kotta, Sadegh (br000070) 2002; 8 Sadegh (br000115) 2001; 46 Karlsruhe, Germany (pp. 1–6). Pommaret (br000100) 2001; Vol. II Halás, Kotta (br000035) 2007; 56 Conte, Moog, Perdon (br000025) 2007 Popov (br000105) 1969; 144 Zheng, Willems, Zhang (br000145) 2001; 46 Rapisarda, Willems (br000110) 1997; 35 Artin (br000010) 1957 Strömberg, Toivonen, Häggiblom, Waller (br000125) 1995; 41 Choquet-Bruhat, DeWitt-Morette, Dillard-Bleick (br000015) 1989 Halás (br000030) 2008; 44 Seoul. Korea (pp. 15197–15202). Stuttgart, Germany (pp. 269–274). Sontag (br000120) 1979; 17 Kotta, Ü. (1998). Lowering the order of input shifts in multi-input discrete-time generalized state-space system. In Zhang, Zheng (br000140) 2004; 77 Kotta, Zinober, Liu (br000090) 2001; 37 Chongqing, China (pp. 529–534). Kotta, Ü., & Tõnso, M. (2004). Irreducibility conditions for discrete-time nonlinear multi-input multi-output systems. In Cohn (br000020) 1965 Halás, M., Kotta, Ü., Li, Z., Wang, H., & Yuan, C. (2009). Submersive rational difference systems and their accessibility. In Kotta, Ü. (1999). Towards a solution of the state-space realization problem of a set of multi-input multi-output nonlinear difference equations. In Tampa, Florida, USA (pp. 4638–4639). Aranda-Bricaire, Kotta, Moog (br000005) 1996; 34 Halás, M., Kotta, Ü., & Moog, C.H. (2008). Transfer function approach to the model matching problem of nonlinear systems. In Wolovich (br000135) 1974 Kotta, Bartosiewicz, Nõmm, Pawluszewicz (br000085) 2011; 56 Kotta, Ü., & Tõnso, M. (2008). Realization of discrete-time nonlinear input–output equations: polynomial approach. In McConnel, Robson (br000095) 1987 Kotta, Mullari (br000065) 2006; 55 Toth, R., Willems, J.C., Heuberger, P.S.C., & van der Hof, P.M.J. (2009). A behavioral approach to lpv systems. In (pp. 175–182). Budapest, Hungary (pp. 2015–2020). Popov (10.1016/j.automatica.2011.07.010_br000105) 1969; 144 Wolovich (10.1016/j.automatica.2011.07.010_br000135) 1974 10.1016/j.automatica.2011.07.010_br000045 Aranda-Bricaire (10.1016/j.automatica.2011.07.010_br000005) 1996; 34 Choquet-Bruhat (10.1016/j.automatica.2011.07.010_br000015) 1989 Kotta (10.1016/j.automatica.2011.07.010_br000065) 2006; 55 Strömberg (10.1016/j.automatica.2011.07.010_br000125) 1995; 41 Cohn (10.1016/j.automatica.2011.07.010_br000020) 1965 Conte (10.1016/j.automatica.2011.07.010_br000025) 2007 10.1016/j.automatica.2011.07.010_br000080 Artin (10.1016/j.automatica.2011.07.010_br000010) 1957 Halás (10.1016/j.automatica.2011.07.010_br000030) 2008; 44 Sontag (10.1016/j.automatica.2011.07.010_br000120) 1979; 17 10.1016/j.automatica.2011.07.010_br000060 Halás (10.1016/j.automatica.2011.07.010_br000040) 2009; 19 Pommaret (10.1016/j.automatica.2011.07.010_br000100) 2001; Vol. II Zheng (10.1016/j.automatica.2011.07.010_br000150) 1995; 2 Zheng (10.1016/j.automatica.2011.07.010_br000145) 2001; 46 Halás (10.1016/j.automatica.2011.07.010_br000035) 2007; 56 Rapisarda (10.1016/j.automatica.2011.07.010_br000110) 1997; 35 Kotta (10.1016/j.automatica.2011.07.010_br000085) 2011; 56 McConnel (10.1016/j.automatica.2011.07.010_br000095) 1987 10.1016/j.automatica.2011.07.010_br000050 Kotta (10.1016/j.automatica.2011.07.010_br000090) 2001; 37 10.1016/j.automatica.2011.07.010_br000055 Sadegh (10.1016/j.automatica.2011.07.010_br000115) 2001; 46 Zhang (10.1016/j.automatica.2011.07.010_br000140) 2004; 77 Kotta (10.1016/j.automatica.2011.07.010_br000070) 2002; 8 10.1016/j.automatica.2011.07.010_br000075 10.1016/j.automatica.2011.07.010_br000130 |
| References_xml | – reference: Toth, R., Willems, J.C., Heuberger, P.S.C., & van der Hof, P.M.J. (2009). A behavioral approach to lpv systems. In – reference: Halás, M., Kotta, Ü., Li, Z., Wang, H., & Yuan, C. (2009). Submersive rational difference systems and their accessibility. In – volume: 34 start-page: 1999 year: 1996 end-page: 2023 ident: br000005 article-title: Linearization of discrete-time systems publication-title: SIAM Journal on Control and Optimization – volume: Vol. II year: 2001 ident: br000100 article-title: Partial differential control theory publication-title: Control systems – volume: 46 start-page: 698 year: 2001 end-page: 710 ident: br000115 article-title: Minimal realization of nonlinear systems described by input–output difference equations publication-title: IEEE Transactions on Automatic Control – reference: Halás, M., Kotta, Ü., & Moog, C.H. (2008). Transfer function approach to the model matching problem of nonlinear systems. In – volume: 2 start-page: 15 year: 1995 end-page: 26 ident: br000150 article-title: Transfer function description for nonlinear systems publication-title: Journal of East China Normal University (Natural Science) – volume: 56 start-page: 322 year: 2007 end-page: 335 ident: br000035 article-title: Transfer functions of discrete-time nonlinear control systems publication-title: Proceedings of the Estonian Academy of Sciences. Physics. Mathematics – volume: 8 start-page: 21 year: 2002 end-page: 32 ident: br000070 article-title: Two approaches for state space realization of narma models: bridging the gap publication-title: Mathematical and Computer Modelling of Dynamical Systems – volume: 17 start-page: 139 year: 1979 end-page: 151 ident: br000120 article-title: On the observability of polynomial systems, i: finite-time problems publication-title: SIAM Journal on Control and Optimization – year: 1965 ident: br000020 article-title: Difference algebra – reference: , Budapest, Hungary (pp. 2015–2020). – year: 1987 ident: br000095 article-title: Noncommutative noetherian rings – reference: , Chongqing, China (pp. 529–534). – volume: 37 start-page: 1771 year: 2001 end-page: 1778 ident: br000090 article-title: Transfer equivalence and realization of nonlinear higher order input–output difference equations publication-title: Automatica – volume: 35 start-page: 1053 year: 1997 end-page: 1091 ident: br000110 article-title: State maps for linear systems publication-title: SIAM Journal on Control and Optimization – reference: , Karlsruhe, Germany (pp. 1–6). – volume: 44 start-page: 1181 year: 2008 end-page: 1190 ident: br000030 article-title: An algebraic framework generalizing the concept of transfer functions to nonlinear systems publication-title: Automatica – reference: Kotta, Ü., & Tõnso, M. (2008). Realization of discrete-time nonlinear input–output equations: polynomial approach. In – reference: , Stuttgart, Germany (pp. 269–274). – volume: 41 start-page: 195 year: 1995 end-page: 199 ident: br000125 article-title: Multivariable nonlinear and adaptive control of a distillation column publication-title: EIChE Journal – volume: 55 start-page: 24 year: 2006 end-page: 42 ident: br000065 article-title: Equivalence of realizability conditions for nonlinear control systems publication-title: Proceedings of the Estonian Academy of Sciences Physics Mathematics – year: 1989 ident: br000015 article-title: Analysis, manifolds and physics, part I: basics – reference: , Seoul. Korea (pp. 15197–15202). – volume: 144 start-page: 169 year: 1969 end-page: 180 ident: br000105 article-title: Some properties of the control systems with irreducible matrix transfer functions publication-title: Lecture Notes in Mathematics – volume: 56 start-page: 1421 year: 2011 end-page: 1426 ident: br000085 article-title: Linear input–output equivalence and row reducedness of discrete-time nonlinear systems publication-title: IEEE Transactions on Automatic Control – year: 2007 ident: br000025 article-title: Algebraic methods for nonlinear control systems – reference: Kotta, Ü., & Tõnso, M. (2004). Irreducibility conditions for discrete-time nonlinear multi-input multi-output systems. In – year: 1974 ident: br000135 article-title: Linear multivariable systems – year: 1957 ident: br000010 article-title: Geometric algebra – reference: , Tampa, Florida, USA (pp. 4638–4639). – reference: Kotta, Ü. (1999). Towards a solution of the state-space realization problem of a set of multi-input multi-output nonlinear difference equations. In – volume: 19 start-page: 451 year: 2009 end-page: 461 ident: br000040 article-title: A note on model matching for nonrealizable nonlinear systems publication-title: Archives of Control Sciences – volume: 46 start-page: 1782 year: 2001 end-page: 1788 ident: br000145 article-title: A polynomial approach to nonlinear system controllability publication-title: IEEE Transactions on Automatic Control – volume: 77 start-page: 491 year: 2004 end-page: 497 ident: br000140 article-title: A polynomial approach to discrete-time nonlinear system controllability publication-title: International Journal of Control – reference: (pp. 175–182). – reference: Kotta, Ü. (1998). Lowering the order of input shifts in multi-input discrete-time generalized state-space system. In – volume: 56 start-page: 322 issue: 4 year: 2007 ident: 10.1016/j.automatica.2011.07.010_br000035 article-title: Transfer functions of discrete-time nonlinear control systems publication-title: Proceedings of the Estonian Academy of Sciences. Physics. Mathematics doi: 10.3176/phys.math.2007.4.04 – volume: 46 start-page: 1782 issue: 11 year: 2001 ident: 10.1016/j.automatica.2011.07.010_br000145 article-title: A polynomial approach to nonlinear system controllability publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.964691 – year: 1965 ident: 10.1016/j.automatica.2011.07.010_br000020 – volume: 34 start-page: 1999 issue: 6 year: 1996 ident: 10.1016/j.automatica.2011.07.010_br000005 article-title: Linearization of discrete-time systems publication-title: SIAM Journal on Control and Optimization doi: 10.1137/S0363012994267315 – ident: 10.1016/j.automatica.2011.07.010_br000045 doi: 10.1145/1576702.1576728 – volume: 19 start-page: 451 issue: 4 year: 2009 ident: 10.1016/j.automatica.2011.07.010_br000040 article-title: A note on model matching for nonrealizable nonlinear systems publication-title: Archives of Control Sciences – volume: 2 start-page: 15 year: 1995 ident: 10.1016/j.automatica.2011.07.010_br000150 article-title: Transfer function description for nonlinear systems publication-title: Journal of East China Normal University (Natural Science) – volume: 56 start-page: 1421 issue: 6 year: 2011 ident: 10.1016/j.automatica.2011.07.010_br000085 article-title: Linear input–output equivalence and row reducedness of discrete-time nonlinear systems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2011.2112430 – year: 1987 ident: 10.1016/j.automatica.2011.07.010_br000095 – year: 1957 ident: 10.1016/j.automatica.2011.07.010_br000010 – ident: 10.1016/j.automatica.2011.07.010_br000060 doi: 10.23919/ECC.1999.7099742 – volume: 35 start-page: 1053 issue: 3 year: 1997 ident: 10.1016/j.automatica.2011.07.010_br000110 article-title: State maps for linear systems publication-title: SIAM Journal on Control and Optimization doi: 10.1137/S0363012994268412 – ident: 10.1016/j.automatica.2011.07.010_br000130 doi: 10.23919/ECC.2009.7074700 – year: 1989 ident: 10.1016/j.automatica.2011.07.010_br000015 – year: 2007 ident: 10.1016/j.automatica.2011.07.010_br000025 – ident: 10.1016/j.automatica.2011.07.010_br000080 doi: 10.1109/WCICA.2008.4592979 – volume: 41 start-page: 195 year: 1995 ident: 10.1016/j.automatica.2011.07.010_br000125 article-title: Multivariable nonlinear and adaptive control of a distillation column publication-title: EIChE Journal – volume: 44 start-page: 1181 issue: 5 year: 2008 ident: 10.1016/j.automatica.2011.07.010_br000030 article-title: An algebraic framework generalizing the concept of transfer functions to nonlinear systems publication-title: Automatica doi: 10.1016/j.automatica.2007.09.008 – volume: Vol. II year: 2001 ident: 10.1016/j.automatica.2011.07.010_br000100 article-title: Partial differential control theory – volume: 46 start-page: 698 issue: 5 year: 2001 ident: 10.1016/j.automatica.2011.07.010_br000115 article-title: Minimal realization of nonlinear systems described by input–output difference equations publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.920788 – volume: 37 start-page: 1771 issue: 11 year: 2001 ident: 10.1016/j.automatica.2011.07.010_br000090 article-title: Transfer equivalence and realization of nonlinear higher order input–output difference equations publication-title: Automatica doi: 10.1016/S0005-1098(01)00144-3 – ident: 10.1016/j.automatica.2011.07.010_br000055 doi: 10.1109/CDC.1998.762064 – year: 1974 ident: 10.1016/j.automatica.2011.07.010_br000135 – volume: 8 start-page: 21 issue: 1 year: 2002 ident: 10.1016/j.automatica.2011.07.010_br000070 article-title: Two approaches for state space realization of narma models: bridging the gap publication-title: Mathematical and Computer Modelling of Dynamical Systems doi: 10.1076/mcmd.8.1.21.8340 – volume: 55 start-page: 24 issue: 1 year: 2006 ident: 10.1016/j.automatica.2011.07.010_br000065 article-title: Equivalence of realizability conditions for nonlinear control systems publication-title: Proceedings of the Estonian Academy of Sciences Physics Mathematics doi: 10.3176/phys.math.2006.1.03 – ident: 10.1016/j.automatica.2011.07.010_br000050 doi: 10.3182/20080706-5-KR-1001.02570 – volume: 144 start-page: 169 year: 1969 ident: 10.1016/j.automatica.2011.07.010_br000105 article-title: Some properties of the control systems with irreducible matrix transfer functions publication-title: Lecture Notes in Mathematics doi: 10.1007/BFb0059934 – ident: 10.1016/j.automatica.2011.07.010_br000075 doi: 10.1016/S1474-6670(17)31232-6 – volume: 17 start-page: 139 year: 1979 ident: 10.1016/j.automatica.2011.07.010_br000120 article-title: On the observability of polynomial systems, i: finite-time problems publication-title: SIAM Journal on Control and Optimization doi: 10.1137/0317011 – volume: 77 start-page: 491 year: 2004 ident: 10.1016/j.automatica.2011.07.010_br000140 article-title: A polynomial approach to discrete-time nonlinear system controllability publication-title: International Journal of Control doi: 10.1080/00207170410001682506 |
| SSID | ssj0004182 |
| Score | 2.173776 |
| Snippet | The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 255 |
| SubjectTerms | Applied sciences Computation Computer science; control theory; systems Control system analysis Control theory. Systems Differentials Discrete-time systems Dynamical systems Equivalence Exact sciences and technology Input–output models Mathematical analysis Modelling and identification Nonlinear control systems Nonlinearity Polynomial methods Reduction Representations State space realization System theory |
| Title | Realization of discrete-time nonlinear input–output equations: Polynomial approach |
| URI | https://dx.doi.org/10.1016/j.automatica.2011.07.010 https://www.proquest.com/docview/1019625225 |
| Volume | 48 |
| WOSCitedRecordID | wos000301213200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-2836 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004182 issn: 0005-1098 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Li9swEBZttoeWUvqk6WNxofSyuNjyQ1J7CiVLW5Z0WRLITTiyDLsstje2S_rvO2PJj7AtpIdenGAsPzTj8Sfpm28Iea85E5wibVBlqQv4P3a5yoTr-xmge7VhG6raYhNsseDrtTi31UartpwAy3O-24nyv5oa9oGxMXX2H8zdnxR2wH8wOmzB7LA9yPAXAP1sciUiQUy73QIydrGK_ElulDGQeZqXTe0WTQ0_J_rGKH63_Ljz4voXJiujioBVHB9D2FlTF63Oa9JKle4MO37gbBe1AaQrXBIYJrHzqrC5QZd7Uw3I2ehpG134RNlSUza6C58hH7kJHcdCo79rP6vUBN1bEdtMHlwhX8fevNVVZR89S3jdE8le_JCnq7MzuZyvlx_KGxfrh-E6uy2mcpccURYJPiFHs2_z9fchR9bnRjnePoJldRmu358v_jeo8rBMKniBMlP55NZHvEUmy8fkkR1SODPjCk_IHZ0_JQ9GQpPPyMXIKZwic_acwumdwhk7hdM7xSdncAmnc4nnZHU6X3756tpqGq4KQ1a7WnCWxqkfC5FSukGkmKUbGgtPp56naBJTZAQHaZBoJiKqMMk-g7fVi0XEUi94QSZwP_olcQJPCZXRUMPgIORwTBoq6sdRorlKAqGmhHUdJ5WVmseKJ9ey4xReyaHLJXa59JiELp8Sv29ZGrmVA9p87mwjLWw0cFCCjx3Q-njPnP1lceaEw3BpSt519pUQenE9Lcl10VR4XhFTGMBErw445jW5P7xTb8ik3jb6LbmnftaX1fbYuutv5cqqvg |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Realization+of+discrete-time+nonlinear+input-output+equations%3A+Polynomial+approach&rft.jtitle=Automatica+%28Oxford%29&rft.au=Kotta%2C+Uelle&rft.au=Tonso%2C+Maris&rft.date=2012-02-01&rft.issn=0005-1098&rft.volume=48&rft.issue=2&rft.spage=255&rft.epage=262&rft_id=info:doi/10.1016%2Fj.automatica.2011.07.010&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0005-1098&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0005-1098&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0005-1098&client=summon |