Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay
This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded time‐varying delays and subject to bounded control constraints. We propose an efficient methodology rooted in linear programming (LP) to des...
Saved in:
| Published in | Optimal control applications & methods |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
15.08.2025
|
| Online Access | Get full text |
| ISSN | 0143-2087 1099-1514 |
| DOI | 10.1002/oca.70015 |
Cover
| Abstract | This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded time‐varying delays and subject to bounded control constraints. We propose an efficient methodology rooted in linear programming (LP) to design stabilizing state feedback controllers. The core contributions include the development of novel characterizations for system positivity and the comparison principle tailored to this specific class of DDEs. Based on these characterizations, we establish sufficient conditions for the existence of admissible state feedback controllers that guarantee both positivity and asymptotic stability of the closed‐loop system while respecting the control input constraints. Crucially, these conditions are formulated as a set of linear inequalities, rendering the controller design problem solvable via standard LP techniques. The effectiveness and practical applicability of the theoretical results are demonstrated through comprehensive numerical examples. |
|---|---|
| AbstractList | This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded time‐varying delays and subject to bounded control constraints. We propose an efficient methodology rooted in linear programming (LP) to design stabilizing state feedback controllers. The core contributions include the development of novel characterizations for system positivity and the comparison principle tailored to this specific class of DDEs. Based on these characterizations, we establish sufficient conditions for the existence of admissible state feedback controllers that guarantee both positivity and asymptotic stability of the closed‐loop system while respecting the control input constraints. Crucially, these conditions are formulated as a set of linear inequalities, rendering the controller design problem solvable via standard LP techniques. The effectiveness and practical applicability of the theoretical results are demonstrated through comprehensive numerical examples. |
| Author | Sau, N. H. Niamsup, P. Phat, V. N. |
| Author_xml | – sequence: 1 givenname: N. H. orcidid: 0000-0002-0123-543X surname: Sau fullname: Sau, N. H. organization: Faculty of Fundamental Sciences Hanoi University of Industry Hanoi Vietnam – sequence: 2 givenname: P. orcidid: 0000-0003-2616-8605 surname: Niamsup fullname: Niamsup, P. organization: Department of Mathematics, Faculty of Science Chiang Mai University Chiang Mai Thailand – sequence: 3 givenname: V. N. orcidid: 0000-0001-9467-6674 surname: Phat fullname: Phat, V. N. organization: ICRTM Institute of Mathematics, VAST Hanoi Vietnam |
| BookMark | eNo1kMtKAzEYRoMo2FYXvkG2Lqbmn0tmsixtvUDBghaXw5-ZpI1Mk5qkQgXBR_AZfRJr1dXHB4ezOH1ybJ1VhFwAGwJj6ZVrcFgyBsUR6QETIoEC8mPSY5BnScqq8pT0Q3hmjJWQpT3yPjNWoadz75Ye12tjl3S02XiHzYpGR8fOhuhxD7X0IaI0nXnDaJylTtO5CyaaV0UnRmvllY0Gu6-Pz__bKDp92R7wQJ9MXNGFlW5r271sojrcnZETjV1Q5387IIvr6eP4Npnd39yNR7OkAQExKYXIU0Ali7wBFKmSWmmRcyFKyQvZVoWWPON5BZzzSjdVJkVRlMhbkUtkkA3I5a-38S4Er3S98WaNflcDq3-61ftu9aFb9g0i5mWu |
| Cites_doi | 10.1080/00207179.2018.1537519 10.1103/PhysRevLett.91.094101 10.1002/9781118033029 10.1109/TAC.2010.2041982 10.1016/j.automatica.2018.03.055 10.1002/oca.2663 10.1080/00207179.2017.1326628 10.1177/1077546309341100 10.1016/j.automatica.2015.04.007 10.1109/81.739268 10.3166/ejc.11.586-600 10.1007/978-3-319-65919-0 10.1007/BFb0002475 10.1016/j.jfranklin.2022.04.001 10.1109/TAC.2009.2017961 10.1016/j.aml.2014.07.003 10.1109/ISEMC.1994.385629 10.1016/j.neunet.2010.06.009 10.1016/0167-2789(94)90043-4 10.1016/j.sysconle.2018.04.008 10.1371/journal.pcbi.1002264 10.23919/ACC.2018.8430869 10.1006/jdeq.1993.1048 10.1109/TAC.2014.2344295 10.1007/s00285-002-0191-5 10.1137/060671425 10.1002/oca.2352 10.1109/TAC.2018.2866467 10.1002/oca.2237 10.4171/017 10.1080/02331934.2010.506535 10.1016/j.sysconle.2018.05.009 10.1049/iet-cta.2018.5150 10.1002/mma.7098 10.1080/02331934.2015.1051534 10.1002/rnc.1604 10.1016/j.automatica.2018.04.026 10.1137/060673813 10.1007/s00034-018-0943-0 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION |
| DOI | 10.1002/oca.70015 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1099-1514 |
| ExternalDocumentID | 10_1002_oca_70015 |
| GroupedDBID | -~X .3N .GA 05W 0R~ 10A 123 1L6 1OB 1OC 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANLZ AAONW AAXRX AAYCA AAYXX AAZKR ABCQN ABCUV ABIJN ABJNI ABPVW ACAHQ ACCZN ACGFS ACPOU ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFWVQ AFZJQ AGHNM AGXDD AGYGG AHBTC AIDQK AIDYY AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ATUGU AUFTA AZBYB AZVAB BAFTC BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CITATION CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS F00 F01 F04 G-S G.N GNP GODZA H.T H.X HBH HGLYW HHY HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LITHE LOXES LP6 LP7 LUTES LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D Q.N Q11 QB0 QRW R.K ROL RX1 SUPJJ TN5 UB1 V2E W8V W99 WBKPD WH7 WIH WIK WLBEL WOHZO WQJ WXSBR WYISQ XG1 XPP XV2 ZZTAW ~IA ~WT |
| ID | FETCH-LOGICAL-c191t-799421aeb54c1a92ebfef946997b65bd85fb6364816668fc83b9557a6d94ba013 |
| ISSN | 0143-2087 |
| IngestDate | Wed Oct 01 05:38:28 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c191t-799421aeb54c1a92ebfef946997b65bd85fb6364816668fc83b9557a6d94ba013 |
| ORCID | 0000-0002-0123-543X 0000-0003-2616-8605 0000-0001-9467-6674 |
| ParticipantIDs | crossref_primary_10_1002_oca_70015 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2025-08-15 |
| PublicationDateYYYYMMDD | 2025-08-15 |
| PublicationDate_xml | – month: 08 year: 2025 text: 2025-08-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationTitle | Optimal control applications & methods |
| PublicationYear | 2025 |
| References | Atay F. M. (e_1_2_10_27_1) 2003; 91 Djema W. (e_1_2_10_25_1) 2018 Josic K. (e_1_2_10_23_1) 2011; 7 Cui Y. (e_1_2_10_21_1) 2018; 94 Dai L. (e_1_2_10_3_1) 1989 Liu X. (e_1_2_10_13_1) 2010; 55 De Iuliis V. (e_1_2_10_36_1) 2019; 64 Phat V. N. (e_1_2_10_38_1) 2014; 38 Briat C. (e_1_2_10_18_1) 2018; 91 Ploskas N. (e_1_2_10_41_1) 2017 Lam J. (e_1_2_10_2_1) 2006 Wang F. (e_1_2_10_7_1) 2016; 37 Yue D. (e_1_2_10_47_1) 2004 Domoshnitsky A. (e_1_2_10_15_1) 2018; 18 Hale J. K. (e_1_2_10_5_1) 2013 Liu M. (e_1_2_10_46_1) 2019; 38 Kunkel P. (e_1_2_10_4_1) 2006 Gu K. (e_1_2_10_8_1) 2011; 21 Roesch O. (e_1_2_10_26_1) 2005; 3 Hui Q. (e_1_2_10_43_1) 2005; 11 Elloumi W. (e_1_2_10_22_1) 2022; 41 Michiels W. (e_1_2_10_29_1) 2009; 48 Rami A. M. (e_1_2_10_17_1) 2007; 54 Sau N. H. (e_1_2_10_10_1) 2022; 359 Liu G. (e_1_2_10_35_1) 2017; 39 Sau N. H. (e_1_2_10_44_1) 2021; 44 Liu X. (e_1_2_10_16_1) 2009; 54 Bellen A. (e_1_2_10_33_1) 1999; 46 Sipahi R. (e_1_2_10_30_1) 2007; 68 Jessop R. (e_1_2_10_32_1) 2010; 23 Shen J. (e_1_2_10_37_1) 2015; 57 Ruehli A. E. (e_1_2_10_34_1) 1994 Farina L. (e_1_2_10_11_1) 2000 Kyrychko Y. (e_1_2_10_45_1) 2010; 16 Tardella F. (e_1_2_10_19_1) 2011; 60 Phat V. N. (e_1_2_10_20_1) 2018; 13 Gopalsamy K. (e_1_2_10_31_1) 1994; 76 Virnik E. (e_1_2_10_12_1) 2008 Liu G. (e_1_2_10_14_1) 2021; 42 Feng Q. (e_1_2_10_6_1) 2018; 116 Shao L. (e_1_2_10_42_1) 2016; 65 Ngoc P. H. A. (e_1_2_10_9_1) 2020; 93 Pathirana N. P. (e_1_2_10_40_1) 2018; 92 Culshaw R. V. (e_1_2_10_24_1) 2003; 46 Kuang Y. (e_1_2_10_28_1) 1993; 103 Shen J. (e_1_2_10_39_1) 2015; 60 |
| References_xml | – volume: 93 start-page: 1920 year: 2020 ident: e_1_2_10_9_1 article-title: Stability of Coupled Functional Differential‐Difference Equations publication-title: International Journal of Control doi: 10.1080/00207179.2018.1537519 – volume: 91 issue: 9 year: 2003 ident: e_1_2_10_27_1 article-title: Distributed Delays Facilitate Amplitude Death of Coupled Oscillators publication-title: Physical Review Letters doi: 10.1103/PhysRevLett.91.094101 – volume-title: Positive Linear Systems, Theory and Applications year: 2000 ident: e_1_2_10_11_1 doi: 10.1002/9781118033029 – volume: 55 start-page: 1024 year: 2010 ident: e_1_2_10_13_1 article-title: Stability Analysis for Continuous‐Time Positive Systems With Time‐Varying Delays publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2010.2041982 – volume: 92 start-page: 259 year: 2018 ident: e_1_2_10_40_1 article-title: Stability of Positive Coupled Differential‐Difference Equations With Unbounded Time‐Varying Delays publication-title: Automatica doi: 10.1016/j.automatica.2018.03.055 – volume: 42 start-page: 81 year: 2021 ident: e_1_2_10_14_1 article-title: Stabilization of Positive Coupled Differential‐Difference Equations With Unbounded Time‐Varying Delays publication-title: Optimal Control Applications & Methods doi: 10.1002/oca.2663 – volume: 91 start-page: 1669 year: 2018 ident: e_1_2_10_18_1 article-title: Stability and Performance Analysis of Linear Positive Systems With Delays Using Input‐Output Methods publication-title: International Journal of Control doi: 10.1080/00207179.2017.1326628 – volume: 16 start-page: 943 year: 2010 ident: e_1_2_10_45_1 article-title: On the Use of Delay Equations in Engineering Applications publication-title: Journal of Vibration and Control doi: 10.1177/1077546309341100 – volume: 57 start-page: 123 year: 2015 ident: e_1_2_10_37_1 article-title: Positivity and Stability of Coupled Differential‐Difference Equations With Time‐Varying Delays publication-title: Automatica doi: 10.1016/j.automatica.2015.04.007 – volume-title: Robust Control and Filtering of Singular Systems year: 2006 ident: e_1_2_10_2_1 – volume: 46 start-page: 212 year: 1999 ident: e_1_2_10_33_1 article-title: Methods for Linear Systems of Circuit Delay Differential Equations of Neutral Type publication-title: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications doi: 10.1109/81.739268 – volume: 11 start-page: 586 year: 2005 ident: e_1_2_10_43_1 article-title: Adaptive Control of Mammillary Drug Delivery Systems With Actuator Amplitude Constraints and System Time Delays publication-title: European Journal of Control doi: 10.3166/ejc.11.586-600 – volume-title: Linear Programming Using MATLAB year: 2017 ident: e_1_2_10_41_1 doi: 10.1007/978-3-319-65919-0 – volume-title: Introduction to Functional Differential Equations year: 2013 ident: e_1_2_10_5_1 – volume-title: Singular Control Systems year: 1989 ident: e_1_2_10_3_1 doi: 10.1007/BFb0002475 – volume: 359 start-page: 4587 year: 2022 ident: e_1_2_10_10_1 article-title: State Bounding for Linear Positive Singular Discrete Systems With Unbounded Time‐Varying Delay publication-title: Journal of the Franklin Institute doi: 10.1016/j.jfranklin.2022.04.001 – volume: 54 start-page: 1596 year: 2009 ident: e_1_2_10_16_1 article-title: Constrained Control of Positive Systems With Delays publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2009.2017961 – volume: 38 start-page: 67 year: 2014 ident: e_1_2_10_38_1 article-title: On Exponential Stability of Linear Singular Positive Delayed Systems publication-title: Applied Mathematics Letters doi: 10.1016/j.aml.2014.07.003 – start-page: 371 volume-title: Proceedings of IEEE Symposium on Electromagnetic Compatibility year: 1994 ident: e_1_2_10_34_1 doi: 10.1109/ISEMC.1994.385629 – volume: 23 start-page: 1187 issue: 10 year: 2010 ident: e_1_2_10_32_1 article-title: Approximating the Stability Region of a Neural Network With a General Distribution of Delays publication-title: Neural Networks doi: 10.1016/j.neunet.2010.06.009 – volume-title: Analysis of Positive Descriptor Systems: Topics in Systems and Control Theory year: 2008 ident: e_1_2_10_12_1 – volume: 3 start-page: 1648 year: 2005 ident: e_1_2_10_26_1 article-title: Remote Control of Mechatronic Systems Over Communication Networks publication-title: IEEE International Conference on Mechatronics and Automation – volume: 41 start-page: 223 year: 2022 ident: e_1_2_10_22_1 article-title: Mohamed Bahloul, Exponential Stability and Stabilization of Positive T‐S Fuzzy Delayed Systems publication-title: Optimal Control Applications and Methods – volume: 76 start-page: 344 issue: 4 year: 1994 ident: e_1_2_10_31_1 article-title: Stability in Asymmetric Hopfield Nets With Transmission Delays publication-title: Physica D: Nonlinear Phenomena doi: 10.1016/0167-2789(94)90043-4 – volume: 116 start-page: 56 year: 2018 ident: e_1_2_10_6_1 article-title: Dissipative Delay Range Analysis of Coupled Differential‐Difference Delay Systems With Distributed Delays publication-title: Systems & Control Letters doi: 10.1016/j.sysconle.2018.04.008 – volume: 7 issue: 11 year: 2011 ident: e_1_2_10_23_1 article-title: Stochastic Delay Accelerates Signaling in Gene Networks publication-title: PLoS Computational Biology doi: 10.1371/journal.pcbi.1002264 – start-page: 1220 volume-title: 2018 Annual American Control Conference (ACC) year: 2018 ident: e_1_2_10_25_1 doi: 10.23919/ACC.2018.8430869 – volume: 103 start-page: 221 issue: 2 year: 1993 ident: e_1_2_10_28_1 article-title: Global Stability for Infinite Delay Lotka‐Volterra Type Systems publication-title: Journal of Differential Equations doi: 10.1006/jdeq.1993.1048 – volume: 60 start-page: 857 year: 2015 ident: e_1_2_10_39_1 article-title: l∞/L∞−Gain Analysis for Positive Linear Systems With Unbounded Time‐Varying Delays publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2014.2344295 – volume: 46 start-page: 425 issue: 5 year: 2003 ident: e_1_2_10_24_1 article-title: A Mathematical Model of Cell‐To‐Cell Spread of HIV‐1 That Includes a Time Delay publication-title: Journal of Mathematical Biology doi: 10.1007/s00285-002-0191-5 – volume: 48 start-page: 77 issue: 1 year: 2009 ident: e_1_2_10_29_1 article-title: Consensus Problems With Distributed Delays, With Application to Traffic Flow Models publication-title: SIAM Journal on Control and Optimization doi: 10.1137/060671425 – volume: 39 start-page: 377 issue: 1 year: 2017 ident: e_1_2_10_35_1 article-title: Mixed H∞$$ {\mathrm{H}}_{\infty } $$ and Passive Filtering for a Class of Singular Systems With Interval Time‐Varying Delays publication-title: Optimal Control Applications & Methods doi: 10.1002/oca.2352 – volume: 64 start-page: 2514 year: 2019 ident: e_1_2_10_36_1 article-title: Internally Positive Representations and Stability Analysis of Coupled Differential‐Difference Systems With Time‐Varying Delays publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2018.2866467 – volume: 37 start-page: 1282 issue: 6 year: 2016 ident: e_1_2_10_7_1 article-title: Optimal Control for Discrete‐Time Singular Stochastic Systems With Input Delay publication-title: Optimal Control Applications and Methods doi: 10.1002/oca.2237 – volume-title: Differential‐Algebraic Equations. Analysis and Numerical Solution year: 2006 ident: e_1_2_10_4_1 doi: 10.4171/017 – start-page: 685 volume-title: Proceedings of the American Control Conference year: 2004 ident: e_1_2_10_47_1 – volume: 54 start-page: 5151 year: 2007 ident: e_1_2_10_17_1 article-title: Controller Synthesis for Positive Linear Systems With Controls publication-title: IEEE Transactions on Circuits and Systems Part II: Express Briefs – volume: 60 start-page: 283 year: 2011 ident: e_1_2_10_19_1 article-title: The Fundamental Theorem of Linear Programming: Extensions and Applications publication-title: Optimization doi: 10.1080/02331934.2010.506535 – volume: 18 start-page: 44 year: 2018 ident: e_1_2_10_15_1 article-title: Positivity for Non‐Metzler Systems and Its Applications to Stability of Time‐Varying Delay Systems publication-title: Systems & Control Letters doi: 10.1016/j.sysconle.2018.05.009 – volume: 13 start-page: 905 year: 2018 ident: e_1_2_10_20_1 article-title: Exponential Stabilization of Positive Singular Linear Discrete‐Time Delay Systems With Bounded Control publication-title: IET Control Theory & Applications doi: 10.1049/iet-cta.2018.5150 – volume: 44 start-page: 5133 year: 2021 ident: e_1_2_10_44_1 article-title: Linear Functional State Bounding for Linear Positive Singular Systems With Disturbances Varying Within a Bounded Set publication-title: Mathematical Methods in the Applied Sciences doi: 10.1002/mma.7098 – volume: 65 start-page: 415 year: 2016 ident: e_1_2_10_42_1 article-title: Primal and Dual Multi‐Objective Linear Programming Algorithms for Linear Multiplicative Programmes publication-title: Optimization doi: 10.1080/02331934.2015.1051534 – volume: 21 start-page: 429 year: 2011 ident: e_1_2_10_8_1 article-title: Small Gain Problem in Coupled Differential‐Difference Equations, Time‐Varying Delays, and Direct Lyapunov Method publication-title: International Journal of Robust and Nonlinear Control doi: 10.1002/rnc.1604 – volume: 94 start-page: 170 year: 2018 ident: e_1_2_10_21_1 article-title: Stability Analysis for Positive Singular Systems With Distributed Delays publication-title: Automatica doi: 10.1016/j.automatica.2018.04.026 – volume: 68 start-page: 738 issue: 3 year: 2007 ident: e_1_2_10_30_1 article-title: Stability of Traffic Flow Behavior With Distributed Delays Modeling the Memory Effects of the Drivers publication-title: SIAM Journal on Applied Mathematics doi: 10.1137/060673813 – volume: 38 start-page: 1639 year: 2019 ident: e_1_2_10_46_1 article-title: On the Stability Analysis of Systems of Neutral Delay Differential Equations publication-title: Circuits, Systems, and Signal Processing doi: 10.1007/s00034-018-0943-0 |
| SSID | ssj0007132 |
| Score | 2.3740585 |
| SecondaryResourceType | online_first |
| Snippet | This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded... |
| SourceID | crossref |
| SourceType | Index Database |
| Title | Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library - Core collection (SURFmarket) issn: 0143-2087 databaseCode: DR2 dateStart: 19960101 customDbUrl: isFulltext: true eissn: 1099-1514 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007132 providerName: Wiley-Blackwell |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Pb9MwFLdKd4HDNDYQjA1Z025TSpvYTnxEW6cKia2CFnqislNbHNY_G8mlEhIfgc_IJ-HZThwXeihcospK0ijvF79_v_ceQudkxhknIo1UT-uIaHBQMibA58kysD-kUkyYOOT7GzYYk3cTOmm1vgSspbKQnXy9ta7kf6QKayBXUyX7D5L1N4UF-A3yhSNIGI47yRgcSdOHZ-g4VnMb4Vg1NVJmGKcdAeGMSkODXXsLcWjZWoY2VI1IgU_9zlMf6kX46vv3ZUWX-2xituOFNJOYlCEw34mNpPAtbD9z22_E0d_D5LiFmBtX7a34j6J0xV4Xg06THxHzb6Udmjf0i8OvwuqKTx04OYxTxNQEXl2lpg9dJiC9Sr0qt92a_qBgc5Ctm7lrDgsqvWOS47TRWHWW_g9F5umFrhVzPIVLp_bSR2gvThkzEy6uPjTtxcBBjx3F1T1Z3XmqG7_x_xrYK4HhMTpA-5XHgN868T9FLbU4RE-CPpJH6LsDAg6AgGsg4GKJAyDgDSDgpcY1EHAIhF8_fjYQwB4C2EAAewhgC4FnaHzdH10OomquRpSDd15EKeck7gklKcl7gsdKaqU5YZynklE5y6iWLGHEppQznWeJ5JSmgs04kQJ8hueovVgu1AuEWZrMZK-ba6HMIIZcCCrgplzwjCh4uy_RWf32pivXPmX6l3SOdznpFXrcoOoEtYuHUp2CPVjI11aovwFZUmS0 |
| linkProvider | Wiley-Blackwell |
| 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=Linear+Programming+Approach+to+Constrained+Stabilization+of+Positive+Differential%E2%80%90Difference+Equations+With+Unbounded+Delay&rft.jtitle=Optimal+control+applications+%26+methods&rft.au=Sau%2C+N.+H.&rft.au=Niamsup%2C+P.&rft.au=Phat%2C+V.+N.&rft.date=2025-08-15&rft.issn=0143-2087&rft.eissn=1099-1514&rft_id=info:doi/10.1002%2Foca.70015&rft.externalDBID=n%2Fa&rft.externalDocID=10_1002_oca_70015 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0143-2087&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0143-2087&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0143-2087&client=summon |