Positive Forms and Stability of Linear Time-Delay Systems
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit paramet...
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| Format: | Conference item |
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2007
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| _version_ | 1826295378882854912 |
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| author | Peet, M Papachristodoulou, A Lall, S |
| author_facet | Peet, M Papachristodoulou, A Lall, S |
| author_sort | Peet, M |
| collection | OXFORD |
| description | We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit parametrization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program. |
| first_indexed | 2024-03-07T04:00:05Z |
| format | Conference item |
| id | oxford-uuid:c4436b44-a186-4c2d-9518-9514ece4c487 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:00:05Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:c4436b44-a186-4c2d-9518-9514ece4c4872022-03-27T06:22:09ZPositive Forms and Stability of Linear Time-Delay SystemsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c4436b44-a186-4c2d-9518-9514ece4c487Symplectic Elements at Oxford2007Peet, MPapachristodoulou, ALall, SWe consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit parametrization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program. |
| spellingShingle | Peet, M Papachristodoulou, A Lall, S Positive Forms and Stability of Linear Time-Delay Systems |
| title | Positive Forms and Stability of Linear Time-Delay Systems |
| title_full | Positive Forms and Stability of Linear Time-Delay Systems |
| title_fullStr | Positive Forms and Stability of Linear Time-Delay Systems |
| title_full_unstemmed | Positive Forms and Stability of Linear Time-Delay Systems |
| title_short | Positive Forms and Stability of Linear Time-Delay Systems |
| title_sort | positive forms and stability of linear time delay systems |
| work_keys_str_mv | AT peetm positiveformsandstabilityoflineartimedelaysystems AT papachristodouloua positiveformsandstabilityoflineartimedelaysystems AT lalls positiveformsandstabilityoflineartimedelaysystems |