Stability and assignment of spectrum in systems with discrete time lags
The asymptotic stability with a prescribed degree of time delayed systems subject to multiple bounded discrete delays has received important attention in the last years. It is basically proved that the α-stability locally in the delays (i.e., all the eigenvalues have prefixed strictly negative real...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/76361 |
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| _version_ | 1850176910467792896 |
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| author | M. De la Sen |
| author_facet | M. De la Sen |
| author_sort | M. De la Sen |
| collection | DOAJ |
| description | The asymptotic stability with a prescribed degree of time delayed
systems subject to multiple bounded discrete delays has received
important attention in the last years. It is basically proved that the α-stability locally in the delays (i.e., all the eigenvalues have
prefixed strictly negative real parts located in Res≤−α<0) may be tested for a set of admissible delays
including possible zero delays either through a set of Lyapunov's
matrix inequalities or, equivalently, by checking that an
identical number of matrices related to the delayed dynamics
are all stability matrices. The result may be easily
extended to check the ε-asymptotic stability independent of the delays, that is, for all the delays having any
values, the eigenvalues are stable and located in Res≤ε→0−. The above referred number of stable matrices to be tested is 2r for a set of distinct r point delays and includes all possible
cases of alternate signs for summations for all the matrices of
delayed dynamics. The manuscript is
completed with a study for prescribed closed-loop spectrum
assignment (or “pole placement”) under output feedback. |
| format | Article |
| id | doaj-art-af4b85e1120c4719b7ecc0de1f4f01cb |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-af4b85e1120c4719b7ecc0de1f4f01cb2025-08-20T02:19:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/7636176361Stability and assignment of spectrum in systems with discrete time lagsM. De la Sen0Instituto de Investigacion y Desarrollo de Procesos (IIDP), Departamento de Electricidad y Electrónica, Facultad de Ciencias, Universidad del País Vasco, Leioa (Bizkaia), Aptdo, 644 de Bilbao, Bilbao 48080, SpainThe asymptotic stability with a prescribed degree of time delayed systems subject to multiple bounded discrete delays has received important attention in the last years. It is basically proved that the α-stability locally in the delays (i.e., all the eigenvalues have prefixed strictly negative real parts located in Res≤−α<0) may be tested for a set of admissible delays including possible zero delays either through a set of Lyapunov's matrix inequalities or, equivalently, by checking that an identical number of matrices related to the delayed dynamics are all stability matrices. The result may be easily extended to check the ε-asymptotic stability independent of the delays, that is, for all the delays having any values, the eigenvalues are stable and located in Res≤ε→0−. The above referred number of stable matrices to be tested is 2r for a set of distinct r point delays and includes all possible cases of alternate signs for summations for all the matrices of delayed dynamics. The manuscript is completed with a study for prescribed closed-loop spectrum assignment (or “pole placement”) under output feedback.http://dx.doi.org/10.1155/DDNS/2006/76361 |
| spellingShingle | M. De la Sen Stability and assignment of spectrum in systems with discrete time lags Discrete Dynamics in Nature and Society |
| title | Stability and assignment of spectrum in systems with discrete time lags |
| title_full | Stability and assignment of spectrum in systems with discrete time lags |
| title_fullStr | Stability and assignment of spectrum in systems with discrete time lags |
| title_full_unstemmed | Stability and assignment of spectrum in systems with discrete time lags |
| title_short | Stability and assignment of spectrum in systems with discrete time lags |
| title_sort | stability and assignment of spectrum in systems with discrete time lags |
| url | http://dx.doi.org/10.1155/DDNS/2006/76361 |
| work_keys_str_mv | AT mdelasen stabilityandassignmentofspectruminsystemswithdiscretetimelags |