Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control
By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. First, based on Kronecker product and Lyapunov functional, some easy-to-test sufficient condition is...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/418258 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550695271661568 |
|---|---|
| author | Kun Yuan Abdulaziz Alofi Jinde Cao Abdullah Al-Mazrooei Ahmed Elaiw |
| author_facet | Kun Yuan Abdulaziz Alofi Jinde Cao Abdullah Al-Mazrooei Ahmed Elaiw |
| author_sort | Kun Yuan |
| collection | DOAJ |
| description | By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. First, based on Kronecker product and Lyapunov functional, some easy-to-test sufficient condition is given to ensure the synchronization of coupled DPS with time delay. Secondly, in the case that the whole coupled system cannot synchronize by itself, the proportional-spatial derivative (P-sD) state feedback controller is designed and applied to force the network to synchronize. The sufficient condition on the existence of synchronization controller is given in terms of a set of linear matrix inequalities. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations. |
| format | Article |
| id | doaj-art-5a8387f6f6b24daf827d3e1af58aecf2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5a8387f6f6b24daf827d3e1af58aecf22025-02-03T06:06:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/418258418258Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative ControlKun Yuan0Abdulaziz Alofi1Jinde Cao2Abdullah Al-Mazrooei3Ahmed Elaiw4School of Automation and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaSchool of Automation and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaBy combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. First, based on Kronecker product and Lyapunov functional, some easy-to-test sufficient condition is given to ensure the synchronization of coupled DPS with time delay. Secondly, in the case that the whole coupled system cannot synchronize by itself, the proportional-spatial derivative (P-sD) state feedback controller is designed and applied to force the network to synchronize. The sufficient condition on the existence of synchronization controller is given in terms of a set of linear matrix inequalities. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.http://dx.doi.org/10.1155/2014/418258 |
| spellingShingle | Kun Yuan Abdulaziz Alofi Jinde Cao Abdullah Al-Mazrooei Ahmed Elaiw Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control Discrete Dynamics in Nature and Society |
| title | Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control |
| title_full | Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control |
| title_fullStr | Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control |
| title_full_unstemmed | Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control |
| title_short | Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control |
| title_sort | synchronization of the coupled distributed parameter system with time delay via proportional spatial derivative control |
| url | http://dx.doi.org/10.1155/2014/418258 |
| work_keys_str_mv | AT kunyuan synchronizationofthecoupleddistributedparametersystemwithtimedelayviaproportionalspatialderivativecontrol AT abdulazizalofi synchronizationofthecoupleddistributedparametersystemwithtimedelayviaproportionalspatialderivativecontrol AT jindecao synchronizationofthecoupleddistributedparametersystemwithtimedelayviaproportionalspatialderivativecontrol AT abdullahalmazrooei synchronizationofthecoupleddistributedparametersystemwithtimedelayviaproportionalspatialderivativecontrol AT ahmedelaiw synchronizationofthecoupleddistributedparametersystemwithtimedelayviaproportionalspatialderivativecontrol |