Controllability and Observability of Nonautonomous Riesz-Spectral Systems
There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/4210135 |
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| author | Sutrima Sutrima Christiana Rini Indrati Lina Aryati |
| author_facet | Sutrima Sutrima Christiana Rini Indrati Lina Aryati |
| author_sort | Sutrima Sutrima |
| collection | DOAJ |
| description | There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a C0-quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively. |
| format | Article |
| id | doaj-art-ca9a47fc9bd748288c5de98e2fd75182 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ca9a47fc9bd748288c5de98e2fd751822025-02-03T00:59:56ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/42101354210135Controllability and Observability of Nonautonomous Riesz-Spectral SystemsSutrima Sutrima0Christiana Rini Indrati1Lina Aryati2Mathematics Department, Universitas Sebelas Maret, Surakarta, IndonesiaMathematics Department, Universitas Gadjah Mada, Yogyakarta, IndonesiaMathematics Department, Universitas Gadjah Mada, Yogyakarta, IndonesiaThere are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a C0-quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.http://dx.doi.org/10.1155/2018/4210135 |
| spellingShingle | Sutrima Sutrima Christiana Rini Indrati Lina Aryati Controllability and Observability of Nonautonomous Riesz-Spectral Systems Abstract and Applied Analysis |
| title | Controllability and Observability of Nonautonomous Riesz-Spectral Systems |
| title_full | Controllability and Observability of Nonautonomous Riesz-Spectral Systems |
| title_fullStr | Controllability and Observability of Nonautonomous Riesz-Spectral Systems |
| title_full_unstemmed | Controllability and Observability of Nonautonomous Riesz-Spectral Systems |
| title_short | Controllability and Observability of Nonautonomous Riesz-Spectral Systems |
| title_sort | controllability and observability of nonautonomous riesz spectral systems |
| url | http://dx.doi.org/10.1155/2018/4210135 |
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