Positivity of kernel functions for systems with communication delay
The purpose of this paper is to provide further results on a method of constructing Lyapunov functionals for infinite-dimensional systems using semidefinite programming. Specifically, we give a necessary and sufficient condition for positivity of a positive integral operator described by a polynomia...
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| Format: | Conference item |
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2007
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| _version_ | 1797056589700530176 |
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| author | Peet, M Papachristodoulou, A IEEE |
| author_facet | Peet, M Papachristodoulou, A IEEE |
| author_sort | Peet, M |
| collection | OXFORD |
| description | The purpose of this paper is to provide further results on a method of constructing Lyapunov functionals for infinite-dimensional systems using semidefinite programming. Specifically, we give a necessary and sufficient condition for positivity of a positive integral operator described by a polynomial kernel. We then show how to combine this result with multiplier operators in order to obtain positive composite Lyapunov functionals. These types of functionals are used to prove stability of linear time-delay systems. © 2007 IEEE. |
| first_indexed | 2024-03-06T19:24:43Z |
| format | Conference item |
| id | oxford-uuid:1b4fad9e-61db-4d97-87dd-2b0460c41931 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:24:43Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:1b4fad9e-61db-4d97-87dd-2b0460c419312022-03-26T10:59:41ZPositivity of kernel functions for systems with communication delayConference itemhttp://purl.org/coar/resource_type/c_5794uuid:1b4fad9e-61db-4d97-87dd-2b0460c41931Symplectic Elements at Oxford2007Peet, MPapachristodoulou, AIEEEThe purpose of this paper is to provide further results on a method of constructing Lyapunov functionals for infinite-dimensional systems using semidefinite programming. Specifically, we give a necessary and sufficient condition for positivity of a positive integral operator described by a polynomial kernel. We then show how to combine this result with multiplier operators in order to obtain positive composite Lyapunov functionals. These types of functionals are used to prove stability of linear time-delay systems. © 2007 IEEE. |
| spellingShingle | Peet, M Papachristodoulou, A IEEE Positivity of kernel functions for systems with communication delay |
| title | Positivity of kernel functions for systems with communication delay |
| title_full | Positivity of kernel functions for systems with communication delay |
| title_fullStr | Positivity of kernel functions for systems with communication delay |
| title_full_unstemmed | Positivity of kernel functions for systems with communication delay |
| title_short | Positivity of kernel functions for systems with communication delay |
| title_sort | positivity of kernel functions for systems with communication delay |
| work_keys_str_mv | AT peetm positivityofkernelfunctionsforsystemswithcommunicationdelay AT papachristodouloua positivityofkernelfunctionsforsystemswithcommunicationdelay AT ieee positivityofkernelfunctionsforsystemswithcommunicationdelay |