On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays
This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/231710 |
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| author | M. de la Sen A. Ibeas |
| author_facet | M. de la Sen A. Ibeas |
| author_sort | M. de la Sen |
| collection | DOAJ |
| description | This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set. |
| format | Article |
| id | doaj-art-54f379c03bcd44199a6ae6dc0af66eba |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-54f379c03bcd44199a6ae6dc0af66eba2025-02-03T05:53:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/231710231710On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point DelaysM. de la Sen0A. Ibeas1Department of Electricity and Electronics, Faculty of Science and Technology, University of Basque, Campus of Leioa (Bizkaia), Aptdo. 644, 48080 Bilbao, SpainDepartment of Telecommunication and Systems Engineering, Engineering School, Autonomous University of Barcelona, Cerdanyola del Vallés, 08193 Bellaterra, Barcelona, SpainThis paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.http://dx.doi.org/10.1155/2008/231710 |
| spellingShingle | M. de la Sen A. Ibeas On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays Discrete Dynamics in Nature and Society |
| title | On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays |
| title_full | On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays |
| title_fullStr | On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays |
| title_full_unstemmed | On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays |
| title_short | On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays |
| title_sort | on the global asymptotic stability of switched linear time varying systems with constant point delays |
| url | http://dx.doi.org/10.1155/2008/231710 |
| work_keys_str_mv | AT mdelasen ontheglobalasymptoticstabilityofswitchedlineartimevaryingsystemswithconstantpointdelays AT aibeas ontheglobalasymptoticstabilityofswitchedlineartimevaryingsystemswithconstantpointdelays |