About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma
This paper formulates an “ad hoc” robust version under parametrical disturbances of the discrete version of the Kalman-Yakubovich-Popov Lemma for a class of positive hybrid dynamic linear systems which consist of a continuous-time system coupled with a discrete-time or a digital one. An extended dis...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/3928970 |
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| _version_ | 1849685889306853376 |
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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 formulates an “ad hoc” robust version under parametrical disturbances of the discrete version of the Kalman-Yakubovich-Popov Lemma for a class of positive hybrid dynamic linear systems which consist of a continuous-time system coupled with a discrete-time or a digital one. An extended discrete system, whose state vector contains both the digital one and the discretization of the continuous-time one at sampling instants, is a key analysis element in the formulation. The hyperstability and asymptotic hyperstability properties of the studied class of positive hybrid systems under feedback from any member of a nonlinear (and, eventually, time-varying) class of controllers, which satisfies a Popov’s-type inequality, are also investigated as linked to the positive realness of the associated transfer matrices. |
| format | Article |
| id | doaj-art-bbeabc4e113e4828a35c74ddc29e942c |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bbeabc4e113e4828a35c74ddc29e942c2025-08-20T03:22:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/39289703928970About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov LemmaM. De la Sen0Instituto de Investigación y Desarrollo de Procesos (IIDP), Facultad de Ciencia y Tecnologia, Universidad del País Vasco, Leioa (Bizkaia), P.O. Box 644 de Bilbao, 48080 Bilbao, SpainThis paper formulates an “ad hoc” robust version under parametrical disturbances of the discrete version of the Kalman-Yakubovich-Popov Lemma for a class of positive hybrid dynamic linear systems which consist of a continuous-time system coupled with a discrete-time or a digital one. An extended discrete system, whose state vector contains both the digital one and the discretization of the continuous-time one at sampling instants, is a key analysis element in the formulation. The hyperstability and asymptotic hyperstability properties of the studied class of positive hybrid systems under feedback from any member of a nonlinear (and, eventually, time-varying) class of controllers, which satisfies a Popov’s-type inequality, are also investigated as linked to the positive realness of the associated transfer matrices.http://dx.doi.org/10.1155/2017/3928970 |
| spellingShingle | M. De la Sen About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma Discrete Dynamics in Nature and Society |
| title | About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma |
| title_full | About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma |
| title_fullStr | About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma |
| title_full_unstemmed | About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma |
| title_short | About a Class of Positive Hybrid Dynamic Linear Systems and an Associate Extended Kalman-Yakubovich-Popov Lemma |
| title_sort | about a class of positive hybrid dynamic linear systems and an associate extended kalman yakubovich popov lemma |
| url | http://dx.doi.org/10.1155/2017/3928970 |
| work_keys_str_mv | AT mdelasen aboutaclassofpositivehybriddynamiclinearsystemsandanassociateextendedkalmanyakubovichpopovlemma |