Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach
In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a co...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/3791609 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565093167005696 |
|---|---|
| author | Sutrima Sutrima Christiana Rini Indrati Lina Aryati |
| author_facet | Sutrima Sutrima Christiana Rini Indrati Lina Aryati |
| author_sort | Sutrima Sutrima |
| collection | DOAJ |
| description | In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated C0-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability. |
| format | Article |
| id | doaj-art-47664f0db6974df4bdbb794bae90c56d |
| 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-47664f0db6974df4bdbb794bae90c56d2025-02-03T01:09:28ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/37916093791609Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup ApproachSutrima Sutrima0Christiana Rini Indrati1Lina Aryati2Mathematics Department of Universitas Sebelas Maret, Surakarta, IndonesiaMathematics Department of Universitas Gadjah Mada, Yogyakarta, IndonesiaMathematics Department of Universitas Gadjah Mada, Yogyakarta, IndonesiaIn the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated C0-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.http://dx.doi.org/10.1155/2018/3791609 |
| spellingShingle | Sutrima Sutrima Christiana Rini Indrati Lina Aryati Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach Abstract and Applied Analysis |
| title | Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach |
| title_full | Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach |
| title_fullStr | Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach |
| title_full_unstemmed | Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach |
| title_short | Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach |
| title_sort | exact null controllability stabilizability and detectability of linear nonautonomous control systems a quasisemigroup approach |
| url | http://dx.doi.org/10.1155/2018/3791609 |
| work_keys_str_mv | AT sutrimasutrima exactnullcontrollabilitystabilizabilityanddetectabilityoflinearnonautonomouscontrolsystemsaquasisemigroupapproach AT christianariniindrati exactnullcontrollabilitystabilizabilityanddetectabilityoflinearnonautonomouscontrolsystemsaquasisemigroupapproach AT linaaryati exactnullcontrollabilitystabilizabilityanddetectabilityoflinearnonautonomouscontrolsystemsaquasisemigroupapproach |