Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions
We consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model. It is shown that the corresponding sampled-data model a...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9154714/ |
| _version_ | 1811273929338126336 |
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| author | Claudia Sanchez Juan I. Yuz |
| author_facet | Claudia Sanchez Juan I. Yuz |
| author_sort | Claudia Sanchez |
| collection | DOAJ |
| description | We consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model. It is shown that the corresponding sampled-data model and its accuracy (measured in terms of the local truncation error) depend on the smoothness of the input and on the applied integration strategy, namely, the truncated Taylor series expansion. Moreover, the sampling zero dynamics of the discrete-time model are asymptotically characterized as the sampling period goes to zero, and it is shown that these zero dynamics converge to the asymptotic sampling zeros of the linear case. |
| first_indexed | 2024-04-12T23:09:45Z |
| format | Article |
| id | doaj.art-bfb1a15da3e749248e034516efa72997 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T23:09:45Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-bfb1a15da3e749248e034516efa729972022-12-22T03:12:50ZengIEEEIEEE Access2169-35362020-01-01814336614337410.1109/ACCESS.2020.30138299154714Approximate Nonlinear Discrete-Time Models Based on B-Spline FunctionsClaudia Sanchez0https://orcid.org/0000-0002-3531-5198Juan I. Yuz1https://orcid.org/0000-0002-9373-7065Department of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaíso, ChileDepartment of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaíso, ChileWe consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model. It is shown that the corresponding sampled-data model and its accuracy (measured in terms of the local truncation error) depend on the smoothness of the input and on the applied integration strategy, namely, the truncated Taylor series expansion. Moreover, the sampling zero dynamics of the discrete-time model are asymptotically characterized as the sampling period goes to zero, and it is shown that these zero dynamics converge to the asymptotic sampling zeros of the linear case.https://ieeexplore.ieee.org/document/9154714/B-spline functionsnonlinear systemsnormal formstruncated Taylor serieszero dynamics |
| spellingShingle | Claudia Sanchez Juan I. Yuz Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions IEEE Access B-spline functions nonlinear systems normal forms truncated Taylor series zero dynamics |
| title | Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions |
| title_full | Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions |
| title_fullStr | Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions |
| title_full_unstemmed | Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions |
| title_short | Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions |
| title_sort | approximate nonlinear discrete time models based on b spline functions |
| topic | B-spline functions nonlinear systems normal forms truncated Taylor series zero dynamics |
| url | https://ieeexplore.ieee.org/document/9154714/ |
| work_keys_str_mv | AT claudiasanchez approximatenonlineardiscretetimemodelsbasedonbsplinefunctions AT juaniyuz approximatenonlineardiscretetimemodelsbasedonbsplinefunctions |