Inverses of positive linear operators and state feedback design for time-delay systems
The problem of designing feedback controllers for dynamical systems with time-delay is addressed in this paper. Previous work has imposed significant restrictions on the structure of the candidate Control Lyapunov Functions in order to develop appropriate LMI conditions for the design. This paper ad...
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| Format: | Conference item |
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2009
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| _version_ | 1797074248953495552 |
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| author | Peet, M Papachristodoulou, A |
| author_facet | Peet, M Papachristodoulou, A |
| author_sort | Peet, M |
| collection | OXFORD |
| description | The problem of designing feedback controllers for dynamical systems with time-delay is addressed in this paper. Previous work has imposed significant restrictions on the structure of the candidate Control Lyapunov Functions in order to develop appropriate LMI conditions for the design. This paper addresses this issue and provides two new results. The first result is a step towards controller synthesis using the \complete quadratic" Lyapunov functional. Specifically, given such a \complete quadratic" functional, defined by polynomials, we give an algorithm for constructing the inverse of the linear operator which defines that functional. Following this, we derive semidefinite programming conditions, expressed as a Sum-of-Squares program, for state feedback synthesis of these systems using a restricted structure of the Lyapunov functional. Copyright © IFAC 2009. |
| first_indexed | 2024-03-06T23:33:24Z |
| format | Conference item |
| id | oxford-uuid:6cd07da7-910f-4b0f-87fd-d993d66a98a1 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:33:24Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:6cd07da7-910f-4b0f-87fd-d993d66a98a12022-03-26T19:13:38ZInverses of positive linear operators and state feedback design for time-delay systemsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:6cd07da7-910f-4b0f-87fd-d993d66a98a1Symplectic Elements at Oxford2009Peet, MPapachristodoulou, AThe problem of designing feedback controllers for dynamical systems with time-delay is addressed in this paper. Previous work has imposed significant restrictions on the structure of the candidate Control Lyapunov Functions in order to develop appropriate LMI conditions for the design. This paper addresses this issue and provides two new results. The first result is a step towards controller synthesis using the \complete quadratic" Lyapunov functional. Specifically, given such a \complete quadratic" functional, defined by polynomials, we give an algorithm for constructing the inverse of the linear operator which defines that functional. Following this, we derive semidefinite programming conditions, expressed as a Sum-of-Squares program, for state feedback synthesis of these systems using a restricted structure of the Lyapunov functional. Copyright © IFAC 2009. |
| spellingShingle | Peet, M Papachristodoulou, A Inverses of positive linear operators and state feedback design for time-delay systems |
| title | Inverses of positive linear operators and state feedback design for time-delay systems |
| title_full | Inverses of positive linear operators and state feedback design for time-delay systems |
| title_fullStr | Inverses of positive linear operators and state feedback design for time-delay systems |
| title_full_unstemmed | Inverses of positive linear operators and state feedback design for time-delay systems |
| title_short | Inverses of positive linear operators and state feedback design for time-delay systems |
| title_sort | inverses of positive linear operators and state feedback design for time delay systems |
| work_keys_str_mv | AT peetm inversesofpositivelinearoperatorsandstatefeedbackdesignfortimedelaysystems AT papachristodouloua inversesofpositivelinearoperatorsandstatefeedbackdesignfortimedelaysystems |