On robustness in the gap metric and coprime factor uncertainty for LTV systems
In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems...
Saved in:
| Published in | Systems & control letters Vol. 80; pp. 16 - 22 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.06.2015
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV Hankel operator, and in which case singular values and vectors can be used to compute the time-varying stability margin and TV controller. |
|---|---|
| AbstractList | In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV Hankel operator, and in which case singular values and vectors can be used to compute the time-varying stability margin and TV controller. |
| Author | Djouadi, Seddik M. |
| Author_xml | – sequence: 1 givenname: Seddik M. surname: Djouadi fullname: Djouadi, Seddik M. email: djouadi@eecs.utk.edu organization: Department of Electrical Engineering and Computer Science, Masdar Institute of Science and Technology, Masdar City, Abu Dhabi, United Arab Emirates |
| BookMark | eNqFkE1LAzEQhoNUsK3-Bckf2DXZ7M52wYNS_IJiL9VryM7OakqblCQV-u_dol689DQMzPPyzjNhI-cdMXYtRS6FhJt1Hg8RvdtQXghZ5ULlQsAZG8tZXWR1U8GIjYfDOoNGygs2iXEthCiEUmP2unQ8-HYfk6MYuXU8fRL_MDu-pRQscuM6jn4X7JZ4bzD5wPcOKSRjXTrwftgXq3c-VEi0jZfsvDebSFe_c8reHh9W8-dssXx6md8vMlSySNmsLRtZQwFYVi3W5awFWRKWhQLqkBpoVEWIJTUIaOqCOtUomNW9aAlAgZoy-MnF4GMM1OtjQxMOWgp9tKLX-s-KPlrRQunBygDe_gPRJpOsdykYuzmN3_3gNDz3ZSnoiJYGH50NhEl33p6K-AYx0IY0 |
| CitedBy_id | crossref_primary_10_1137_16M1092775 crossref_primary_10_2139_ssrn_4096592 crossref_primary_10_1090_proc_14629 crossref_primary_10_1016_j_isatra_2022_03_004 crossref_primary_10_1049_iet_cta_2019_0303 crossref_primary_10_1016_j_sysconle_2023_105569 crossref_primary_10_1137_19M1259390 crossref_primary_10_52547_joc_16_2_41 crossref_primary_10_1109_TCYB_2021_3051368 |
| Cites_doi | 10.1109/9.151094 10.1016/0167-6911(88)90111-9 10.1016/0167-6911(88)90067-9 10.1109/9.53546 10.1109/CDC.2006.377263 10.1137/0331071 10.1016/0024-3795(94)90438-3 10.1016/j.sysconle.2007.04.008 10.1109/CDC.2007.4435030 10.1137/0331072 10.1007/BF01203025 10.1007/BF01211622 10.1109/CDC.2004.1428794 10.1109/CDC.1990.203305 10.1109/9.29424 10.1112/jlms/s2-32.2.272 10.1109/TAC.2002.1000266 10.1016/0167-6911(91)90016-8 |
| ContentType | Journal Article |
| Copyright | 2015 Elsevier B.V. |
| Copyright_xml | – notice: 2015 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.sysconle.2015.03.006 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1872-7956 |
| EndPage | 22 |
| ExternalDocumentID | 10_1016_j_sysconle_2015_03_006 S0167691115000663 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 29Q 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABFNM ABJNI ABMAC ABTAH ABUCO ABXDB ABYKQ ACDAQ ACGFS ACNNM ACRLP ADBBV ADEZE ADIYS ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ APLSM ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HVGLF HZ~ IHE J1W JJJVA KOM LY1 LY7 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SDS SES SET SEW SPC SPCBC SSB SSD SST SSZ T5K TN5 WH7 WUQ XPP ZMT ZY4 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH |
| ID | FETCH-LOGICAL-c312t-8b4917626c45bc748b614ec4236edce96935ecc4e9c6ca72ed393687f0be66363 |
| IEDL.DBID | .~1 |
| ISSN | 0167-6911 |
| IngestDate | Tue Jul 01 03:29:06 EDT 2025 Thu Apr 24 23:03:11 EDT 2025 Fri Feb 23 02:32:48 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Coprime factorization Robust stabilization Time-varying Gap metric |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c312t-8b4917626c45bc748b614ec4236edce96935ecc4e9c6ca72ed393687f0be66363 |
| PageCount | 7 |
| ParticipantIDs | crossref_primary_10_1016_j_sysconle_2015_03_006 crossref_citationtrail_10_1016_j_sysconle_2015_03_006 elsevier_sciencedirect_doi_10_1016_j_sysconle_2015_03_006 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | June 2015 2015-06-00 |
| PublicationDateYYYYMMDD | 2015-06-01 |
| PublicationDate_xml | – month: 06 year: 2015 text: June 2015 |
| PublicationDecade | 2010 |
| PublicationTitle | Systems & control letters |
| PublicationYear | 2015 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Davidson (br000005) 1988 Cantoni, Vinnicombe (br000055) 2002; 47 Zhu, Hautus, Praagman (br000050) 1988; 11 Nagy, Foias (br000120) 1968; 266 Power (br000145) 1985; 2 Georgiou, Smith (br000045) 1992; 37 Georgiou, Smith (br000040) 1990; 35 Feintuch (br000015) 1994; 208 Feintuch (br000070) 1991; 16 Glover, McFarlane (br000095) 1989; 34 Ball (br000135) 1996; 25 Douglas (br000020) 1972 C. Foias, T. Georgiou, M.C. Smith, Geometric techniques for robust stabilization of linear time-varying systems, in: Proc. of he 29th CDC, December 1990, pp. 2868–2873. Nagy, Foias, Bercovici, Kerchy (br000125) 2010 Djouadi, Li (br000090) 2007; 56 Zhou, Doyle (br000105) 1998 S.M. Djouadi, C.D. Charalambous, On optimal performance for linear-time varying systems, in: Proc. of the IEEE 43th Conference on Decision and Control, Paradise Island, Bahamas, December 14–17, 2004, pp. 875–880. Partington (br000130) 2004 S.M. Djouadi, Robustness in the gap metric and coprime factor perturbations for LTV systems, in: 46th IEEE Conference on Date of Conference, New Orleans, LA, December 12–14, 2007, pp. 6400–6405. Feintuch (br000080) 1998 Dale, Smith (br000110) 1993; 31 G. Zames, A.K. El-Sakkary, Unstable systems and feedback: The gap metric, in: Proc. of the Allerton Conference, 1980, pp. 380–385. Feintuch (br000075) 1993; 6 S.M. Djouadi, Y. Li, On robust stabilization in the gap metric for LTV systems, in: Proceedings of the IEEE Conference on Decision and Control, San-Diego December, June 14–26, 2006, pp. 3648–2653–6080. Foias, Georgiou, Smith (br000065) 1993; 31 Georgiou (br000035) 1988; 11 Luenberger (br000025) 1968 Feintuch, Saeks (br000010) 1982 Schatten (br000140) 1960 Georgiou (10.1016/j.sysconle.2015.03.006_br000045) 1992; 37 Foias (10.1016/j.sysconle.2015.03.006_br000065) 1993; 31 Davidson (10.1016/j.sysconle.2015.03.006_br000005) 1988 Dale (10.1016/j.sysconle.2015.03.006_br000110) 1993; 31 10.1016/j.sysconle.2015.03.006_br000030 Feintuch (10.1016/j.sysconle.2015.03.006_br000010) 1982 Nagy (10.1016/j.sysconle.2015.03.006_br000125) 2010 Luenberger (10.1016/j.sysconle.2015.03.006_br000025) 1968 10.1016/j.sysconle.2015.03.006_br000115 Glover (10.1016/j.sysconle.2015.03.006_br000095) 1989; 34 Partington (10.1016/j.sysconle.2015.03.006_br000130) 2004 Douglas (10.1016/j.sysconle.2015.03.006_br000020) 1972 Djouadi (10.1016/j.sysconle.2015.03.006_br000090) 2007; 56 Zhu (10.1016/j.sysconle.2015.03.006_br000050) 1988; 11 Nagy (10.1016/j.sysconle.2015.03.006_br000120) 1968; 266 Feintuch (10.1016/j.sysconle.2015.03.006_br000070) 1991; 16 Schatten (10.1016/j.sysconle.2015.03.006_br000140) 1960 Feintuch (10.1016/j.sysconle.2015.03.006_br000075) 1993; 6 Feintuch (10.1016/j.sysconle.2015.03.006_br000080) 1998 Cantoni (10.1016/j.sysconle.2015.03.006_br000055) 2002; 47 10.1016/j.sysconle.2015.03.006_br000085 Georgiou (10.1016/j.sysconle.2015.03.006_br000035) 1988; 11 10.1016/j.sysconle.2015.03.006_br000060 Georgiou (10.1016/j.sysconle.2015.03.006_br000040) 1990; 35 Power (10.1016/j.sysconle.2015.03.006_br000145) 1985; 2 Feintuch (10.1016/j.sysconle.2015.03.006_br000015) 1994; 208 Ball (10.1016/j.sysconle.2015.03.006_br000135) 1996; 25 Zhou (10.1016/j.sysconle.2015.03.006_br000105) 1998 10.1016/j.sysconle.2015.03.006_br000100 |
| References_xml | – reference: S.M. Djouadi, C.D. Charalambous, On optimal performance for linear-time varying systems, in: Proc. of the IEEE 43th Conference on Decision and Control, Paradise Island, Bahamas, December 14–17, 2004, pp. 875–880. – volume: 16 start-page: 277 year: 1991 end-page: 279 ident: br000070 article-title: The gap metric for time-varying systems publication-title: Systems Control Lett. – volume: 266 start-page: 493 year: 1968 end-page: 495 ident: br000120 article-title: Dilatation des commutants des commutateurs d’operateurs publication-title: C. R. Acad. Sci. Paris, Ser. A – volume: 11 start-page: 253 year: 1988 end-page: 257 ident: br000035 article-title: On the computation of the gap metric publication-title: Systems Control Lett. – volume: 31 start-page: 1518 year: 1993 end-page: 1537 ident: br000065 article-title: Robust stability of feedback systems: A geometric approach using the gap metric publication-title: SIAM J. Control Optim. – year: 2010 ident: br000125 article-title: Harmonic Analysis of Operators on Hilbert Space – volume: 34 start-page: 821 year: 1989 end-page: 830 ident: br000095 article-title: Robust stabilization of normalized coprime factor plant descriptions with publication-title: IEEE Trans. Automat. Control – volume: 35 start-page: 673 year: 1990 end-page: 686 ident: br000040 article-title: Optimal robustness in the gap metric publication-title: IEEE Trans. Automat. Control – reference: S.M. Djouadi, Y. Li, On robust stabilization in the gap metric for LTV systems, in: Proceedings of the IEEE Conference on Decision and Control, San-Diego December, June 14–26, 2006, pp. 3648–2653–6080. – volume: 25 start-page: 377 year: 1996 end-page: 405 ident: br000135 article-title: Commutant lifting and interpolation: The time varying case publication-title: Integral Equations Operator Theory – volume: 208 start-page: 209 year: 1994 end-page: 221 ident: br000015 article-title: The gap metric robustness for linear time-varying systems publication-title: Linear Algebra Appl. – reference: S.M. Djouadi, Robustness in the gap metric and coprime factor perturbations for LTV systems, in: 46th IEEE Conference on Date of Conference, New Orleans, LA, December 12–14, 2007, pp. 6400–6405. – volume: 11 start-page: 53 year: 1988 end-page: 59 ident: br000050 article-title: Sufficient conditions for robust BIBO stabilisation: Given by the gap metric publication-title: Systems Control Lett. – volume: 47 year: 2002 ident: br000055 article-title: Linear feedback systems and the graph topology publication-title: IEEE Trans. Automat. Control – year: 1960 ident: br000140 article-title: Norm Ideals of Completely Continuous Operators – year: 2004 ident: br000130 publication-title: Linear Operators and Linear Systems – volume: 31 start-page: 1538 year: 1993 end-page: 1557 ident: br000110 article-title: Stabilizability and existence of system representation for discrete-time-varying systems publication-title: SIAM J. Control Optim. – year: 1972 ident: br000020 article-title: Banach Algebra Techniques in Operator Theory – volume: 37 start-page: 1133 year: 1992 end-page: 1143 ident: br000045 article-title: Robust stabilization in the gap metric: Controller design for distributed plants publication-title: IEEE Trans. Automat. Control – year: 1998 ident: br000105 article-title: Essentials of Robust Control – volume: 56 start-page: 753 year: 2007 end-page: 758 ident: br000090 article-title: On the computation of the gap metric for LTV systems publication-title: Systems Control Lett. – year: 1998 ident: br000080 article-title: Robust Control Theory in Hilbert Space, Vol. 130 – year: 1988 ident: br000005 article-title: Nest Algebras – reference: C. Foias, T. Georgiou, M.C. Smith, Geometric techniques for robust stabilization of linear time-varying systems, in: Proc. of he 29th CDC, December 1990, pp. 2868–2873. – volume: 2 start-page: 272 year: 1985 end-page: 282 ident: br000145 article-title: Commutators with the triangular projection and hankel forms on nest algebras publication-title: J. Lond. Math. Soc. – year: 1982 ident: br000010 article-title: System Theory: A Hilbert Space Approach – year: 1968 ident: br000025 article-title: Optimization by Vector Space Methods – reference: G. Zames, A.K. El-Sakkary, Unstable systems and feedback: The gap metric, in: Proc. of the Allerton Conference, 1980, pp. 380–385. – volume: 6 start-page: 247 year: 1993 end-page: 263 ident: br000075 article-title: Robustness for time-varying systems publication-title: Math. Control Signals Systems – year: 2010 ident: 10.1016/j.sysconle.2015.03.006_br000125 – year: 1960 ident: 10.1016/j.sysconle.2015.03.006_br000140 – volume: 37 start-page: 1133 issue: 8 year: 1992 ident: 10.1016/j.sysconle.2015.03.006_br000045 article-title: Robust stabilization in the gap metric: Controller design for distributed plants publication-title: IEEE Trans. Automat. Control doi: 10.1109/9.151094 – volume: 11 start-page: 53 year: 1988 ident: 10.1016/j.sysconle.2015.03.006_br000050 article-title: Sufficient conditions for robust BIBO stabilisation: Given by the gap metric publication-title: Systems Control Lett. doi: 10.1016/0167-6911(88)90111-9 – volume: 11 start-page: 253 year: 1988 ident: 10.1016/j.sysconle.2015.03.006_br000035 article-title: On the computation of the gap metric publication-title: Systems Control Lett. doi: 10.1016/0167-6911(88)90067-9 – volume: 35 start-page: 673 issue: 6 year: 1990 ident: 10.1016/j.sysconle.2015.03.006_br000040 article-title: Optimal robustness in the gap metric publication-title: IEEE Trans. Automat. Control doi: 10.1109/9.53546 – ident: 10.1016/j.sysconle.2015.03.006_br000085 doi: 10.1109/CDC.2006.377263 – year: 1998 ident: 10.1016/j.sysconle.2015.03.006_br000105 – volume: 31 start-page: 1518 issue: 6 year: 1993 ident: 10.1016/j.sysconle.2015.03.006_br000065 article-title: Robust stability of feedback systems: A geometric approach using the gap metric publication-title: SIAM J. Control Optim. doi: 10.1137/0331071 – volume: 208 start-page: 209 year: 1994 ident: 10.1016/j.sysconle.2015.03.006_br000015 article-title: The gap metric robustness for linear time-varying systems publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(94)90438-3 – year: 1968 ident: 10.1016/j.sysconle.2015.03.006_br000025 – volume: 56 start-page: 753 issue: 11–12 year: 2007 ident: 10.1016/j.sysconle.2015.03.006_br000090 article-title: On the computation of the gap metric for LTV systems publication-title: Systems Control Lett. doi: 10.1016/j.sysconle.2007.04.008 – ident: 10.1016/j.sysconle.2015.03.006_br000100 doi: 10.1109/CDC.2007.4435030 – year: 1982 ident: 10.1016/j.sysconle.2015.03.006_br000010 – volume: 31 start-page: 1538 issue: 6 year: 1993 ident: 10.1016/j.sysconle.2015.03.006_br000110 article-title: Stabilizability and existence of system representation for discrete-time-varying systems publication-title: SIAM J. Control Optim. doi: 10.1137/0331072 – volume: 266 start-page: 493 year: 1968 ident: 10.1016/j.sysconle.2015.03.006_br000120 article-title: Dilatation des commutants des commutateurs d’operateurs publication-title: C. R. Acad. Sci. Paris, Ser. A – volume: 25 start-page: 377 year: 1996 ident: 10.1016/j.sysconle.2015.03.006_br000135 article-title: Commutant lifting and interpolation: The time varying case publication-title: Integral Equations Operator Theory doi: 10.1007/BF01203025 – year: 1972 ident: 10.1016/j.sysconle.2015.03.006_br000020 – year: 1998 ident: 10.1016/j.sysconle.2015.03.006_br000080 – volume: 6 start-page: 247 year: 1993 ident: 10.1016/j.sysconle.2015.03.006_br000075 article-title: Robustness for time-varying systems publication-title: Math. Control Signals Systems doi: 10.1007/BF01211622 – ident: 10.1016/j.sysconle.2015.03.006_br000115 doi: 10.1109/CDC.2004.1428794 – ident: 10.1016/j.sysconle.2015.03.006_br000060 doi: 10.1109/CDC.1990.203305 – year: 2004 ident: 10.1016/j.sysconle.2015.03.006_br000130 – volume: 34 start-page: 821 year: 1989 ident: 10.1016/j.sysconle.2015.03.006_br000095 article-title: Robust stabilization of normalized coprime factor plant descriptions with H∞-bounded uncertainty publication-title: IEEE Trans. Automat. Control doi: 10.1109/9.29424 – volume: 2 start-page: 272 issue: 32 year: 1985 ident: 10.1016/j.sysconle.2015.03.006_br000145 article-title: Commutators with the triangular projection and hankel forms on nest algebras publication-title: J. Lond. Math. Soc. doi: 10.1112/jlms/s2-32.2.272 – volume: 47 issue: 5 year: 2002 ident: 10.1016/j.sysconle.2015.03.006_br000055 article-title: Linear feedback systems and the graph topology publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2002.1000266 – ident: 10.1016/j.sysconle.2015.03.006_br000030 – year: 1988 ident: 10.1016/j.sysconle.2015.03.006_br000005 – volume: 16 start-page: 277 year: 1991 ident: 10.1016/j.sysconle.2015.03.006_br000070 article-title: The gap metric for time-varying systems publication-title: Systems Control Lett. doi: 10.1016/0167-6911(91)90016-8 |
| SSID | ssj0002033 |
| Score | 2.1873662 |
| Snippet | In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 16 |
| SubjectTerms | Coprime factorization Gap metric Robust stabilization Time-varying |
| Title | On robustness in the gap metric and coprime factor uncertainty for LTV systems |
| URI | https://dx.doi.org/10.1016/j.sysconle.2015.03.006 |
| Volume | 80 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NT8IwFG-IXvRg_Iz4QXrwOrbRrtuOhEhQFBMF5ba0XWcgOBY2Dlz82-2jm2JiwsHTsqUvWX7t3sfye7-H0I2TUL3TglpU59IWJcq3uBsmlvJDHnIS-4GCH_qPA9Yb0fuxN66hTtULA7TK0vcbn7721uUTu0TTziYT-wUI9Ay-Vc8ETuhgpz6c8ubnD82j5Zhx8qDvDas3uoSnzXyV66pzBnKZrmfETtnfAWoj6HQP0UGZLeK2eaEjVFPpMdrf0BA8QYOnFC_mYpkX4LTwJMU6pcPvPMMfMCxLYp7GWM4zkPHHZroO1rHMMAGKFdZJK34YvmIj6ZyfolH3dtjpWeWQBEsSt1VYgaC64tJliaSekD4NhA64SuosiQHBM2Qh8fQ2URVKJrnfUjEJCQv8xBFKg8bIGdpJ56k6R1gKQrhwY-inplQEPPBipiuYJIhdxpOkjrwKmUiWCuIwyGIWVVSxaVQhGgGikUMijWgd2d92mdHQ2GoRVsBHv05DpB39FtuLf9heoj24M1SwK7RTLJbqWicdhWisT1UD7bbv-r0BXPvPb_0vTNjZmg |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV09b8IwED1RGNoOVT9V-umhawrBjpOMCBVB-ehQqNgs23EqEA0RhIF_X7tOEJUqMXRNdFL0bN-9i57fATzVY6JXWhCHaC7tEKx8h7th7Cg_5CHHkR8o80N_MKSdMXmdeJMStIq7MEZWmed-m9N_snX-pJajWUun09q7EdBTc1Y9WzgPoGLcqbwyVJrdXme4TciNup0obyy-TcDOReHZ82qz0o3n3Dhmup71O6V_16idutM-hZOcMKKm_aYzKKnkHI53bAQvYPiWoOVCrFeZyVtomiDN6tAnT9GXmZclEU8iJBepcfJHdsAO0uXMigGyDdK8FfVHH8i6Oq8uYdx-GbU6Tj4nwZHYbWROIIhuunRnIoknpE8CoWuukpooUaPxDGmIPb1SRIWSSu43VIRDTAM_rgulcaP4CsrJIlHXgKTAmAs3MleqCREBD7yI6iYmDiKX8jiuglcgw2RuIm5mWcxZoRabsQJRZhBldcw0olWobeNSa6OxNyIsgGe_NgTTuX5P7M0_Yh_hsDMa9Fm_O-zdwpF5Y5Vhd1DOlmt1rzlIJh7yPfYN9rXaqA |
| 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=On+robustness+in+the+gap+metric+and+coprime+factor+uncertainty+for+LTV+systems&rft.jtitle=Systems+%26+control+letters&rft.au=Djouadi%2C+Seddik+M.&rft.date=2015-06-01&rft.pub=Elsevier+B.V&rft.issn=0167-6911&rft.eissn=1872-7956&rft.volume=80&rft.spage=16&rft.epage=22&rft_id=info:doi/10.1016%2Fj.sysconle.2015.03.006&rft.externalDocID=S0167691115000663 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-6911&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-6911&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-6911&client=summon |