On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems
This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order α. Expressions for the expansions of the evolution operators in powers of the matrix of dynamics are first obtained. Sets of linearly independen...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/846590 |
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| author | M. De la Sen |
| author_facet | M. De la Sen |
| author_sort | M. De la Sen |
| collection | DOAJ |
| description | This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order α. Expressions for the expansions of the evolution operators in powers of the matrix of dynamics are first obtained. Sets of linearly independent continuous functions or matrix functions, which are also Chebyshev's systems, appear in such expansions in a natural way. Based on the properties of such functions, the controllability and observability of the Caputo fractional differential system of real order α are discussed as related to their counterpart properties in the corresponding standard system defined for α=1. Extensions are given to the fulfilment of those properties under non-uniform sampling. It is proved that the choice of the appropriate sampling instants is not restrictive as a result of the properties of the associate Chebyshev's systems. |
| format | Article |
| id | doaj-art-e635eab03f4f44049b666cdb07f2bdca |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e635eab03f4f44049b666cdb07f2bdca2025-08-20T03:26:04ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/846590846590On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant SystemsM. De la Sen0Institute for Research and Development of Processes, Faculty of Science and Technology, University of Basque Country, Campus of Leioa, Aptdo. 544, 48080 Bilbao, SpainThis paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order α. Expressions for the expansions of the evolution operators in powers of the matrix of dynamics are first obtained. Sets of linearly independent continuous functions or matrix functions, which are also Chebyshev's systems, appear in such expansions in a natural way. Based on the properties of such functions, the controllability and observability of the Caputo fractional differential system of real order α are discussed as related to their counterpart properties in the corresponding standard system defined for α=1. Extensions are given to the fulfilment of those properties under non-uniform sampling. It is proved that the choice of the appropriate sampling instants is not restrictive as a result of the properties of the associate Chebyshev's systems.http://dx.doi.org/10.1155/2010/846590 |
| spellingShingle | M. De la Sen On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems Discrete Dynamics in Nature and Society |
| title | On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems |
| title_full | On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems |
| title_fullStr | On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems |
| title_full_unstemmed | On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems |
| title_short | On Chebyshev's Systems and Non-Uniform Sampling Related to Caputo Fractional Dynamic Time-Invariant Systems |
| title_sort | on chebyshev s systems and non uniform sampling related to caputo fractional dynamic time invariant systems |
| url | http://dx.doi.org/10.1155/2010/846590 |
| work_keys_str_mv | AT mdelasen onchebyshevssystemsandnonuniformsamplingrelatedtocaputofractionaldynamictimeinvariantsystems |