Low-rank balanced truncation of discrete time-delay systems based on Laguerre expansions
This paper introduces a novel model order reduction method based on low-rank Gramian approximations for discrete time-delay systems. Firstly, an efficient algorithm based on Laguerre functions to compute the low-rank decomposition factors of the controllability and observability Gramians for discret...
Saved in:
Published in | Journal of the Franklin Institute Vol. 361; no. 6; p. 106752 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.04.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | This paper introduces a novel model order reduction method based on low-rank Gramian approximations for discrete time-delay systems. Firstly, an efficient algorithm based on Laguerre functions to compute the low-rank decomposition factors of the controllability and observability Gramians for discrete time-delay systems is given, in which the low-rank factors satisfy the iterative recursive formulas of the expansion coefficients of the Laguerre functions. It effectively avoids the direct solutions of Gramians. Then, the reduced-order model of the discrete time-delay system is obtained by combining the low-rank square root method. Additionally, a modified algorithm that combines the dominant subspace projection method is introduced, which alleviates certain drawbacks of the above technique and enhances the stability in certain cases. Finally, two numerical examples are given to verify the accuracy and efficiency of our proposed algorithm.
•A low-rank model order reduction algorithm for discrete time-delay systems is presented.•The low-rank factors of the Gramians are calculated iteratively by the Laguerre functions.•An effective strategy is given to produce a stable reduced model under certain conditions.•The efficiency of the proposed algorithm is verified by two given numerical examples. |
---|---|
AbstractList | This paper introduces a novel model order reduction method based on low-rank Gramian approximations for discrete time-delay systems. Firstly, an efficient algorithm based on Laguerre functions to compute the low-rank decomposition factors of the controllability and observability Gramians for discrete time-delay systems is given, in which the low-rank factors satisfy the iterative recursive formulas of the expansion coefficients of the Laguerre functions. It effectively avoids the direct solutions of Gramians. Then, the reduced-order model of the discrete time-delay system is obtained by combining the low-rank square root method. Additionally, a modified algorithm that combines the dominant subspace projection method is introduced, which alleviates certain drawbacks of the above technique and enhances the stability in certain cases. Finally, two numerical examples are given to verify the accuracy and efficiency of our proposed algorithm.
•A low-rank model order reduction algorithm for discrete time-delay systems is presented.•The low-rank factors of the Gramians are calculated iteratively by the Laguerre functions.•An effective strategy is given to produce a stable reduced model under certain conditions.•The efficiency of the proposed algorithm is verified by two given numerical examples. |
ArticleNumber | 106752 |
Author | Fang, Ya-Xin Xiao, Zhi-Hua Qi, Zhen-Zhong |
Author_xml | – sequence: 1 givenname: Ya-Xin surname: Fang fullname: Fang, Ya-Xin organization: School of Information and Mathematics, Yangtze University, Jingzhou, China – sequence: 2 givenname: Zhi-Hua orcidid: 0000-0002-4607-0739 surname: Xiao fullname: Xiao, Zhi-Hua email: zhxiao@yangtzeu.edu.cn organization: School of Information and Mathematics, Yangtze University, Jingzhou, China – sequence: 3 givenname: Zhen-Zhong surname: Qi fullname: Qi, Zhen-Zhong organization: School of Mathematics, Northwest University, Xi’an, China |
BookMark | eNqFkF1LwzAUhoNMcJv-BvsHOpO0S5vLMfwYFLxR8C6cJieS2qUj6dT9e1Mm3np1OIf3eTk8CzLzg0dCbhldMcrEXbfqbAD_0Tu_4pSX6SqqNb8gc1ZXMudCFjMypymaU1rwK7KIsUtrxSidk7dm-MonPGuhB6_RZGM4eg2jG3w22My4qAOOmI1uj7nBHk5ZPMUR9zEhMeVTroH3I4aAGX4fwMeExmtyaaGPePM7l-T14f5l-5Q3z4-77abJNRdszNHW9dq0bF1U0ELLKRYoaWmE5JJJXonWQgpAwQDL1jIQutasaC2nJZPCFEtSnXt1GGIMaNUhuD2Ek2JUTYJUp_4EqUmQOgtK5OZMYnrv02FQUTucFLiAelRmcP92_AD46nbN |
Cites_doi | 10.1016/S0024-3795(02)00283-5 10.1007/s10543-013-0439-z 10.1016/j.jfranklin.2020.08.038 10.1016/S0005-1098(99)00094-1 10.1109/TAC.2018.2830638 10.1109/TCS.1978.1084534 10.1109/22.868996 10.1109/TAC.2016.2635381 10.3182/20140824-6-ZA-1003.00655 10.1016/j.jfranklin.2022.06.032 10.1524/auto.2013.1007 10.1016/j.jfranklin.2016.06.024 10.1137/S0895479801384937 10.1080/00207170410001663525 10.1016/j.laa.2006.01.007 10.1080/00207721.2020.1785578 10.1080/00207170410001713448 10.1142/9789812702289_0005 10.1137/15M1030911 10.1016/j.sysconle.2019.03.004 10.1016/j.laa.2022.12.020 10.1109/TCSI.2013.2295011 10.1023/A:1022205420182 10.1016/j.apm.2022.01.035 10.1109/TAC.2021.3086319 10.1016/j.matcom.2021.06.021 10.1137/100797436 10.1137/S1064827599360091 10.1016/j.jfranklin.2022.07.028 |
ContentType | Journal Article |
Copyright | 2024 The Franklin Institute |
Copyright_xml | – notice: 2024 The Franklin Institute |
DBID | AAYXX CITATION |
DOI | 10.1016/j.jfranklin.2024.106752 |
DatabaseName | CrossRef |
DatabaseTitle | CrossRef |
DatabaseTitleList | |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Engineering |
EISSN | 1879-2693 |
ExternalDocumentID | 10_1016_j_jfranklin_2024_106752 S001600322400173X |
GrantInformation_xml | – fundername: Natural Science of Shaanxi Province, China grantid: 2020JQ-569 funderid: http://dx.doi.org/10.13039/501100010228 – fundername: State Administration of Foreign Experts Affairs (SAFEA), China grantid: G2023027005L funderid: http://dx.doi.org/10.13039/501100003512 – fundername: Shaanxi Provincial Department of Education, China grantid: 19JK0839 funderid: http://dx.doi.org/10.13039/501100009103 – fundername: National Natural Science Foundation of China grantid: 62273059 funderid: http://dx.doi.org/10.13039/501100001809 |
GroupedDBID | --K --M -DZ -~X .~1 0R~ 1B1 1RT 1~. 1~5 29L 4.4 41~ 457 4G. 5GY 5VS 6TJ 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO AAYFN ABAOU ABBOA ABEFU ABFRF ABJNI ABMAC ABTAH ABUCO ABXDB ABYKQ ACAZW ACCUC ACDAQ ACGFO ACGFS ACIWK ACNCT ACNNM ACRLP ACZNC ADEZE ADGUI ADJOM ADMUD ADTZH AEBSH AECPX AEFWE AEKER AETEA AFDAS AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHPAA AHZHX AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR AXJTR BJAXD BKOJK BLXMC CS3 D1Z EBS EFJIC EJD EO8 EO9 EP2 EP3 F5P FA8 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA GBOLZ HAMUX HMJ HVGLF HZ~ H~9 IHE J1W JJJVA KOM LY7 M26 M41 MHUIS MO0 MVM N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SCC SDF SDG SES SET SEW SME SPC SPCBC SSB SSD SST SSV SSW SSZ T5K TN5 UHS VOH WH7 WUQ XOL XPP ZCG ZMT ZY4 ~02 ~G- AAXKI AAYXX AFJKZ CITATION |
ID | FETCH-LOGICAL-c261t-ef885db1537abab20e3e904d692919276bfa85da31ae4bf1a6c8c13bf204196d3 |
IEDL.DBID | AIKHN |
ISSN | 0016-0032 |
IngestDate | Thu Sep 26 17:11:17 EDT 2024 Sat Apr 20 15:59:36 EDT 2024 |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 6 |
Keywords | Balanced truncation Low-rank Gramians Model order reduction Laguerre functions Discrete time-delay systems |
Language | English |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-c261t-ef885db1537abab20e3e904d692919276bfa85da31ae4bf1a6c8c13bf204196d3 |
ORCID | 0000-0002-4607-0739 |
ParticipantIDs | crossref_primary_10_1016_j_jfranklin_2024_106752 elsevier_sciencedirect_doi_10_1016_j_jfranklin_2024_106752 |
PublicationCentury | 2000 |
PublicationDate | April 2024 2024-04-00 |
PublicationDateYYYYMMDD | 2024-04-01 |
PublicationDate_xml | – month: 04 year: 2024 text: April 2024 |
PublicationDecade | 2020 |
PublicationTitle | Journal of the Franklin Institute |
PublicationYear | 2024 |
Publisher | Elsevier Inc |
Publisher_xml | – name: Elsevier Inc |
References | Wang, Jiang, Kong (b18) 2016; 353 Atwell, King (b32) 2004; 26 Samuel, Knockaert, Dhaene (b12) 2014; 61 Brewer (b22) 1978; 25 Knockaert, De Zutter (b20) 2000; 48 Benner, Goyal, Duff (b23) 2021; 67 Wang, Xu, Zhai, Chen, Lin (b4) 2022; 357 Li, White (b28) 2002; 24 Scarciotti, Astolfi (b33) 2014; 47 Gugercin, Sorensen, Antoulas (b26) 2003; 32 Li, Zhao, Wang, Zhang, Shi (b30) 2018; 64 Zhang, He, Jiang, Wu (b31) 2016; 62 Li, Jiang, Yang (b11) 2021; 190 Benner, Kürschner, Saak (b24) 2016; 38 Xiao, Jiang, Qi (b9) 2019; 126 Suh (b25) 1999; 35 Zhang, Su (b34) 2013; 53 Wang, Jiang, Xu (b15) 2020; 51 Michiels, Jarlebring, Meerbergen (b13) 2011; 32 Gugercin, Antoulas (b5) 2004; 77 Wolf, Panzer, Lohmann (b8) 2013; 61 Xiao, Song, Jiang, Qi (b19) 2022; 106 Gao, Lam, Wang, Xu (b17) 2004; 77 Muhammad (b6) 2022; 359 Michiels, Niculescu (b2) 2007 Erneux (b3) 2009 Xu, Jiang, Li, Li (b16) 2023; 661 Michiels, Niculescu (b1) 2014 Li, White (b27) 2001; 11 Sorensen, Antoulas (b7) 2002; 351 Penzl (b21) 2006; 415 Xiao, Fang, Jiang (b10) 2023; 70 D.Lj. Debeljkovic, M.P. Lazarevic, S.P. Stojanovic, M.B. Jovanovic, S.A. Milinkovic, Discrete time delayed system stability theory in the sense of Lyapunov: New results, in: Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004, pp. 511–516. Wang, Cheng (b14) 2022; 359 Sorensen (10.1016/j.jfranklin.2024.106752_b7) 2002; 351 Penzl (10.1016/j.jfranklin.2024.106752_b21) 2006; 415 Gao (10.1016/j.jfranklin.2024.106752_b17) 2004; 77 Li (10.1016/j.jfranklin.2024.106752_b27) 2001; 11 Li (10.1016/j.jfranklin.2024.106752_b11) 2021; 190 Samuel (10.1016/j.jfranklin.2024.106752_b12) 2014; 61 Wang (10.1016/j.jfranklin.2024.106752_b18) 2016; 353 Knockaert (10.1016/j.jfranklin.2024.106752_b20) 2000; 48 Gugercin (10.1016/j.jfranklin.2024.106752_b5) 2004; 77 Michiels (10.1016/j.jfranklin.2024.106752_b13) 2011; 32 Li (10.1016/j.jfranklin.2024.106752_b28) 2002; 24 Scarciotti (10.1016/j.jfranklin.2024.106752_b33) 2014; 47 Wang (10.1016/j.jfranklin.2024.106752_b4) 2022; 357 Gugercin (10.1016/j.jfranklin.2024.106752_b26) 2003; 32 Muhammad (10.1016/j.jfranklin.2024.106752_b6) 2022; 359 Suh (10.1016/j.jfranklin.2024.106752_b25) 1999; 35 10.1016/j.jfranklin.2024.106752_b29 Michiels (10.1016/j.jfranklin.2024.106752_b1) 2014 Atwell (10.1016/j.jfranklin.2024.106752_b32) 2004; 26 Xiao (10.1016/j.jfranklin.2024.106752_b9) 2019; 126 Xu (10.1016/j.jfranklin.2024.106752_b16) 2023; 661 Zhang (10.1016/j.jfranklin.2024.106752_b31) 2016; 62 Li (10.1016/j.jfranklin.2024.106752_b30) 2018; 64 Zhang (10.1016/j.jfranklin.2024.106752_b34) 2013; 53 Wolf (10.1016/j.jfranklin.2024.106752_b8) 2013; 61 Wang (10.1016/j.jfranklin.2024.106752_b14) 2022; 359 Xiao (10.1016/j.jfranklin.2024.106752_b19) 2022; 106 Benner (10.1016/j.jfranklin.2024.106752_b23) 2021; 67 Erneux (10.1016/j.jfranklin.2024.106752_b3) 2009 Xiao (10.1016/j.jfranklin.2024.106752_b10) 2023; 70 Michiels (10.1016/j.jfranklin.2024.106752_b2) 2007 Wang (10.1016/j.jfranklin.2024.106752_b15) 2020; 51 Benner (10.1016/j.jfranklin.2024.106752_b24) 2016; 38 Brewer (10.1016/j.jfranklin.2024.106752_b22) 1978; 25 |
References_xml | – volume: 32 start-page: 27 year: 2003 end-page: 55 ident: b26 article-title: A modified low-rank Smith method for large-scale Lyapunov equations publication-title: Numer. Algorithms contributor: fullname: Antoulas – volume: 357 start-page: 12670 year: 2022 end-page: 12699 ident: b4 article-title: Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems publication-title: J. Franklin Inst. B contributor: fullname: Lin – volume: 77 start-page: 748 year: 2004 end-page: 766 ident: b5 article-title: A survey of model reduction by balanced truncation and some new results publication-title: Internat. J. Control contributor: fullname: Antoulas – volume: 53 start-page: 1047 year: 2013 end-page: 1073 ident: b34 article-title: A memory-efficient model order reduction for time-delay systems publication-title: BIT Numer. Math. contributor: fullname: Su – volume: 64 start-page: 712 year: 2018 end-page: 719 ident: b30 article-title: Necessary and sufficient conditions of exponential stability for delayed linear discrete-time systems publication-title: IEEE Trans. Automat. Control contributor: fullname: Shi – volume: 61 start-page: 1815 year: 2014 end-page: 1823 ident: b12 article-title: Model order reduction of time-delay systems using a laguerre expansion technique publication-title: IEEE Trans. Circuits Syst. I. Regul. Pap. contributor: fullname: Dhaene – volume: 47 start-page: 9462 year: 2014 end-page: 9467 ident: b33 article-title: Model reduction by moment matching for linear time-delay systems publication-title: IFAC Proc. Vol. contributor: fullname: Astolfi – volume: 26 start-page: 128 year: 2004 end-page: 151 ident: b32 article-title: Reduced order controllers for spatially distributed systems via proper orthogonal decomposition publication-title: SIAM J. Sci. Comput. contributor: fullname: King – year: 2009 ident: b3 article-title: Applied Delay Differential Equations contributor: fullname: Erneux – volume: 661 start-page: 222 year: 2023 end-page: 246 ident: b16 article-title: Model reduction of discrete time-delay systems based on charlier polynomials and high-order krylov subspaces publication-title: Linear Algebr. Appl. contributor: fullname: Li – volume: 70 start-page: 3014 year: 2023 end-page: 3018 ident: b10 article-title: Laguerre-based low-rank balanced truncation of discrete-time systems publication-title: IEEE Trans. Circuits Syst. II contributor: fullname: Jiang – volume: 351 start-page: 671 year: 2002 end-page: 700 ident: b7 article-title: The Sylvester equation and approximate balanced reduction publication-title: Linear Algebra Appl. contributor: fullname: Antoulas – volume: 190 start-page: 905 year: 2021 end-page: 920 ident: b11 article-title: Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials publication-title: Math. Comput. Simulation contributor: fullname: Yang – year: 2014 ident: b1 article-title: Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach contributor: fullname: Niculescu – volume: 359 start-page: 6438 year: 2022 end-page: 6466 ident: b6 article-title: Development of time-limited model reduction technique for one-dimensional and two-dimensional systems with error bound via balanced structure publication-title: J. Franklin Inst. B contributor: fullname: Muhammad – volume: 24 start-page: 260 year: 2002 end-page: 280 ident: b28 article-title: Low-rank solution of Lyapunov equations publication-title: SIAM J. Matrix Anal. Appl. contributor: fullname: White – volume: 353 start-page: 3560 year: 2016 end-page: 3577 ident: b18 article-title: Laguerre functions approximation for model reduction of second order time-delay systems publication-title: J. Franklin Inst. B contributor: fullname: Kong – volume: 106 start-page: 100 year: 2022 end-page: 113 ident: b19 article-title: Model order reduction of linear and bilinear systems via low-rank Gramian approximation publication-title: Appl. Math. Model. contributor: fullname: Qi – volume: 77 start-page: 321 year: 2004 end-page: 335 ident: b17 article-title: model reduction for discrete time-delay systems: delay-independent and dependent approaches publication-title: Internat. J. Control contributor: fullname: Xu – volume: 48 start-page: 1469 year: 2000 end-page: 1475 ident: b20 article-title: Laguerre-SVD reduced-order modeling publication-title: IEEE Trans. Microw. Theory Tech. contributor: fullname: De Zutter – volume: 67 start-page: 886 year: 2021 end-page: 893 ident: b23 article-title: Gramians, energy functionals, and balanced truncation for linear dynamical systems with quadratic outputs publication-title: IEEE Trans. Automat. Control contributor: fullname: Duff – volume: 11 start-page: 1151 year: 2001 end-page: 1171 ident: b27 article-title: Reduction of large circuit models via low-rank approximate gramians publication-title: Int. J. Appl. Math. Comput. Sci. contributor: fullname: White – volume: 51 start-page: 2134 year: 2020 end-page: 2149 ident: b15 article-title: Time domain and frequency domain model order reduction for discrete time-delay systems publication-title: Internat. J. Systems Sci. contributor: fullname: Xu – volume: 126 start-page: 48 year: 2019 end-page: 57 ident: b9 article-title: Finite-time balanced truncation for linear systems via shifted Legendre polynomials publication-title: Systems Control Lett. contributor: fullname: Qi – volume: 32 start-page: 1399 year: 2011 end-page: 1421 ident: b13 article-title: Krylov-based model order reduction of time-delay systems publication-title: SIAM J. Matrix Anal. Appl. contributor: fullname: Meerbergen – volume: 38 start-page: A471 year: 2016 end-page: A499 ident: b24 article-title: Frequency-limited balanced truncation with low-rank approximations publication-title: SIAM J. Sci. Comput. contributor: fullname: Saak – volume: 415 start-page: 322 year: 2006 end-page: 343 ident: b21 article-title: Algorithms for model reduction of large dynamical systems publication-title: Linear Algebra Appl. contributor: fullname: Penzl – volume: 359 start-page: 8243 year: 2022 end-page: 8264 ident: b14 article-title: Balanced truncation for discrete time-delay systems via the interpretation of system energy publication-title: J. Franklin Inst. B contributor: fullname: Cheng – volume: 25 start-page: 772 year: 1978 end-page: 781 ident: b22 article-title: Kronecker products and matrix calculus in system theory publication-title: IEEE Trans. Circuits Syst. contributor: fullname: Brewer – volume: 35 start-page: 1855 year: 1999 end-page: 1860 ident: b25 article-title: Diagonal balanced truncation of discrete delay systems publication-title: Automatica contributor: fullname: Suh – year: 2007 ident: b2 article-title: Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach contributor: fullname: Niculescu – volume: 61 start-page: 545 year: 2013 end-page: 556 ident: b8 article-title: Model order reduction by approximate balanced truncation: A unifying framework/modellreduktion durch approximatives balanciertes abschneiden: Eine vereinigende formulierung publication-title: at-Automatisierungstechnik contributor: fullname: Lohmann – volume: 62 start-page: 5331 year: 2016 end-page: 5336 ident: b31 article-title: Notes on stability of time-delay systems: bounding inequalities and augmented Lyapunov-Krasovskii functionals publication-title: IEEE Trans. Automat. Control contributor: fullname: Wu – volume: 351 start-page: 671 year: 2002 ident: 10.1016/j.jfranklin.2024.106752_b7 article-title: The Sylvester equation and approximate balanced reduction publication-title: Linear Algebra Appl. doi: 10.1016/S0024-3795(02)00283-5 contributor: fullname: Sorensen – volume: 11 start-page: 1151 year: 2001 ident: 10.1016/j.jfranklin.2024.106752_b27 article-title: Reduction of large circuit models via low-rank approximate gramians publication-title: Int. J. Appl. Math. Comput. Sci. contributor: fullname: Li – volume: 53 start-page: 1047 year: 2013 ident: 10.1016/j.jfranklin.2024.106752_b34 article-title: A memory-efficient model order reduction for time-delay systems publication-title: BIT Numer. Math. doi: 10.1007/s10543-013-0439-z contributor: fullname: Zhang – volume: 357 start-page: 12670 issue: 17 year: 2022 ident: 10.1016/j.jfranklin.2024.106752_b4 article-title: Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems publication-title: J. Franklin Inst. B doi: 10.1016/j.jfranklin.2020.08.038 contributor: fullname: Wang – volume: 35 start-page: 1855 issue: 11 year: 1999 ident: 10.1016/j.jfranklin.2024.106752_b25 article-title: Diagonal balanced truncation of discrete delay systems publication-title: Automatica doi: 10.1016/S0005-1098(99)00094-1 contributor: fullname: Suh – volume: 64 start-page: 712 issue: 2 year: 2018 ident: 10.1016/j.jfranklin.2024.106752_b30 article-title: Necessary and sufficient conditions of exponential stability for delayed linear discrete-time systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2018.2830638 contributor: fullname: Li – volume: 25 start-page: 772 issue: 9 year: 1978 ident: 10.1016/j.jfranklin.2024.106752_b22 article-title: Kronecker products and matrix calculus in system theory publication-title: IEEE Trans. Circuits Syst. doi: 10.1109/TCS.1978.1084534 contributor: fullname: Brewer – volume: 48 start-page: 1469 issue: 9 year: 2000 ident: 10.1016/j.jfranklin.2024.106752_b20 article-title: Laguerre-SVD reduced-order modeling publication-title: IEEE Trans. Microw. Theory Tech. doi: 10.1109/22.868996 contributor: fullname: Knockaert – volume: 62 start-page: 5331 issue: 10 year: 2016 ident: 10.1016/j.jfranklin.2024.106752_b31 article-title: Notes on stability of time-delay systems: bounding inequalities and augmented Lyapunov-Krasovskii functionals publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2016.2635381 contributor: fullname: Zhang – volume: 47 start-page: 9462 issue: 3 year: 2014 ident: 10.1016/j.jfranklin.2024.106752_b33 article-title: Model reduction by moment matching for linear time-delay systems publication-title: IFAC Proc. Vol. doi: 10.3182/20140824-6-ZA-1003.00655 contributor: fullname: Scarciotti – volume: 359 start-page: 6438 issue: 12 year: 2022 ident: 10.1016/j.jfranklin.2024.106752_b6 article-title: Development of time-limited model reduction technique for one-dimensional and two-dimensional systems with error bound via balanced structure publication-title: J. Franklin Inst. B doi: 10.1016/j.jfranklin.2022.06.032 contributor: fullname: Muhammad – volume: 61 start-page: 545 issue: 8 year: 2013 ident: 10.1016/j.jfranklin.2024.106752_b8 article-title: Model order reduction by approximate balanced truncation: A unifying framework/modellreduktion durch approximatives balanciertes abschneiden: Eine vereinigende formulierung publication-title: at-Automatisierungstechnik doi: 10.1524/auto.2013.1007 contributor: fullname: Wolf – volume: 70 start-page: 3014 issue: 8 year: 2023 ident: 10.1016/j.jfranklin.2024.106752_b10 article-title: Laguerre-based low-rank balanced truncation of discrete-time systems publication-title: IEEE Trans. Circuits Syst. II contributor: fullname: Xiao – volume: 353 start-page: 3560 issue: 14 year: 2016 ident: 10.1016/j.jfranklin.2024.106752_b18 article-title: Laguerre functions approximation for model reduction of second order time-delay systems publication-title: J. Franklin Inst. B doi: 10.1016/j.jfranklin.2016.06.024 contributor: fullname: Wang – year: 2014 ident: 10.1016/j.jfranklin.2024.106752_b1 contributor: fullname: Michiels – volume: 24 start-page: 260 issue: 1 year: 2002 ident: 10.1016/j.jfranklin.2024.106752_b28 article-title: Low-rank solution of Lyapunov equations publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479801384937 contributor: fullname: Li – volume: 77 start-page: 321 issue: 4 year: 2004 ident: 10.1016/j.jfranklin.2024.106752_b17 article-title: H∞ model reduction for discrete time-delay systems: delay-independent and dependent approaches publication-title: Internat. J. Control doi: 10.1080/00207170410001663525 contributor: fullname: Gao – volume: 415 start-page: 322 issue: 2–3 year: 2006 ident: 10.1016/j.jfranklin.2024.106752_b21 article-title: Algorithms for model reduction of large dynamical systems publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2006.01.007 contributor: fullname: Penzl – volume: 51 start-page: 2134 issue: 12 year: 2020 ident: 10.1016/j.jfranklin.2024.106752_b15 article-title: Time domain and frequency domain model order reduction for discrete time-delay systems publication-title: Internat. J. Systems Sci. doi: 10.1080/00207721.2020.1785578 contributor: fullname: Wang – volume: 77 start-page: 748 issue: 8 year: 2004 ident: 10.1016/j.jfranklin.2024.106752_b5 article-title: A survey of model reduction by balanced truncation and some new results publication-title: Internat. J. Control doi: 10.1080/00207170410001713448 contributor: fullname: Gugercin – ident: 10.1016/j.jfranklin.2024.106752_b29 doi: 10.1142/9789812702289_0005 – volume: 38 start-page: A471 issue: 1 year: 2016 ident: 10.1016/j.jfranklin.2024.106752_b24 article-title: Frequency-limited balanced truncation with low-rank approximations publication-title: SIAM J. Sci. Comput. doi: 10.1137/15M1030911 contributor: fullname: Benner – volume: 126 start-page: 48 year: 2019 ident: 10.1016/j.jfranklin.2024.106752_b9 article-title: Finite-time balanced truncation for linear systems via shifted Legendre polynomials publication-title: Systems Control Lett. doi: 10.1016/j.sysconle.2019.03.004 contributor: fullname: Xiao – volume: 661 start-page: 222 year: 2023 ident: 10.1016/j.jfranklin.2024.106752_b16 article-title: Model reduction of discrete time-delay systems based on charlier polynomials and high-order krylov subspaces publication-title: Linear Algebr. Appl. doi: 10.1016/j.laa.2022.12.020 contributor: fullname: Xu – volume: 61 start-page: 1815 issue: 6 year: 2014 ident: 10.1016/j.jfranklin.2024.106752_b12 article-title: Model order reduction of time-delay systems using a laguerre expansion technique publication-title: IEEE Trans. Circuits Syst. I. Regul. Pap. doi: 10.1109/TCSI.2013.2295011 contributor: fullname: Samuel – volume: 32 start-page: 27 issue: 1 year: 2003 ident: 10.1016/j.jfranklin.2024.106752_b26 article-title: A modified low-rank Smith method for large-scale Lyapunov equations publication-title: Numer. Algorithms doi: 10.1023/A:1022205420182 contributor: fullname: Gugercin – volume: 106 start-page: 100 year: 2022 ident: 10.1016/j.jfranklin.2024.106752_b19 article-title: Model order reduction of linear and bilinear systems via low-rank Gramian approximation publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2022.01.035 contributor: fullname: Xiao – volume: 67 start-page: 886 issue: 2 year: 2021 ident: 10.1016/j.jfranklin.2024.106752_b23 article-title: Gramians, energy functionals, and balanced truncation for linear dynamical systems with quadratic outputs publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2021.3086319 contributor: fullname: Benner – volume: 190 start-page: 905 year: 2021 ident: 10.1016/j.jfranklin.2024.106752_b11 article-title: Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials publication-title: Math. Comput. Simulation doi: 10.1016/j.matcom.2021.06.021 contributor: fullname: Li – volume: 32 start-page: 1399 issue: 4 year: 2011 ident: 10.1016/j.jfranklin.2024.106752_b13 article-title: Krylov-based model order reduction of time-delay systems publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/100797436 contributor: fullname: Michiels – volume: 26 start-page: 128 issue: 1 year: 2004 ident: 10.1016/j.jfranklin.2024.106752_b32 article-title: Reduced order controllers for spatially distributed systems via proper orthogonal decomposition publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827599360091 contributor: fullname: Atwell – year: 2007 ident: 10.1016/j.jfranklin.2024.106752_b2 contributor: fullname: Michiels – volume: 359 start-page: 8243 issue: 15 year: 2022 ident: 10.1016/j.jfranklin.2024.106752_b14 article-title: Balanced truncation for discrete time-delay systems via the interpretation of system energy publication-title: J. Franklin Inst. B doi: 10.1016/j.jfranklin.2022.07.028 contributor: fullname: Wang – year: 2009 ident: 10.1016/j.jfranklin.2024.106752_b3 contributor: fullname: Erneux |
SSID | ssj0017100 |
Score | 2.4186552 |
Snippet | This paper introduces a novel model order reduction method based on low-rank Gramian approximations for discrete time-delay systems. Firstly, an efficient... |
SourceID | crossref elsevier |
SourceType | Aggregation Database Publisher |
StartPage | 106752 |
SubjectTerms | Balanced truncation Discrete time-delay systems Laguerre functions Low-rank Gramians Model order reduction |
Title | Low-rank balanced truncation of discrete time-delay systems based on Laguerre expansions |
URI | https://dx.doi.org/10.1016/j.jfranklin.2024.106752 |
Volume | 361 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED6VssCAeIrykgdWUyd2XmxVBSrPCaRuke2cUTu0VVsELPx2zjitqITEwJjIJyefc9_dOXdngPMoFQpVHvFUFY4CFJvxQmjHE4mkH5J00Ppq5IfHtPesbvtJvwHdRS2MT6usuT9w-jdb13faNZrtyWDga3xpIiG_syCjTPbXYJ3MkVJNWO_c3PUelz8TfAObQMgUPJPASprX0NWHo1OsGKsL31EtiX83Uj8Mz_U2bNUeI-uEh9qBBo52YfNHH8E96N-P37ifgBmfqUgvxebT11HYjWNjx3zt7ZTcY-aPkue-MeQHCz2cZ8zbsYrRuHv98orTKTJ8J4rwu2izfXi-vnrq9nh9ZAK3FArNObo8TypDNJZpo00sUGIhVJWSF0S-XJYap2mAlpFGZVykU5vbSBoXC0W6WMkDaI7GIzwEllemSjKJwlKIhpjmNhcai9jaQhdOYQvEAqNyEjpjlIuUsWG5hLX0sJYB1hZcLrAsVxa5JP7-S_joP8LHsOGvQsrNCTRpEfCUvIm5OYO1i8_orP5mvgBbKstI |
link.rule.ids | 315,786,790,4521,24144,27955,27956,45618,45712 |
linkProvider | Elsevier |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELZKGYAB8RTl6YE1rRM7LzZUgQq0nVqpW2Q7Z9QOaZW2AhZ-O-cmqVoJiYE1seXk7PvuzvrujpB7N2ACROQ6gYgNBig6dGImjeNzQP3gqIPaZiP3-kFnKF5H_qhG2lUujKVVlthfYPoKrcsnrVKardl4bHN8cSHGVyxIN-SjHbJrvQHL62p-r3keri1fU8Axhs44fIvkNTFla3SMFD3RtPXUfO93E7Vhdp6PyGHpL9LH4pOOSQ2yE3KwUUXwlIy60w_HLkCV5SniL9FFvsyKuzg6NdRm3uboHFPbSN6xZSG_aFHBeU6tFUspjuvK9yXkOVD4RICwd2jzMzJ8fhq0O07ZMMHRGAgtHDBR5KcKQSyUSiqPAYeYiTRAHwg9uTBQRuIAyV0JQhlXBjrSLlfGYwI1MeXnpJ5NM7ggNEpV6occmMYADSCIdMQkxJ7WsYyNgAZhlYySWVEXI6kIY5NkLdbEijUpxNogD5Usk60tThC9_5p8-Z_Jd2SvM-h1k-5L_-2K7Ns3BfnmmtRxQ-AG_YqFul2dmx8pSswd |
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=Low-rank+balanced+truncation+of+discrete+time-delay+systems+based+on+Laguerre+expansions&rft.jtitle=Journal+of+the+Franklin+Institute&rft.au=Fang%2C+Ya-Xin&rft.au=Xiao%2C+Zhi-Hua&rft.au=Qi%2C+Zhen-Zhong&rft.date=2024-04-01&rft.pub=Elsevier+Inc&rft.issn=0016-0032&rft.eissn=1879-2693&rft.volume=361&rft.issue=6&rft_id=info:doi/10.1016%2Fj.jfranklin.2024.106752&rft.externalDocID=S001600322400173X |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0016-0032&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0016-0032&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0016-0032&client=summon |