On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems
The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almo...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/681523 |
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| author | Sendren Sheng-Dong Xu Chih-Chiang Chen |
| author_facet | Sendren Sheng-Dong Xu Chih-Chiang Chen |
| author_sort | Sendren Sheng-Dong Xu |
| collection | DOAJ |
| description | The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding
the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every
survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence
of two conditions regarding the existence of stabilizing switching laws between two unstable linear
systems. One is effective for theoretical derivation, while the other is implementable, and a class of
stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the
equivalent relation, a condition for the existence of controllers and stabilizing switching laws between
two unstabilizable linear control systems is then proposed. Then, the study is further extended to the
issue concerning the construction of quadratically stabilizing switching laws among unstable linear
systems and unstabilizable linear control systems. The obtained results are employed to study the
existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable
linear control systems. The numerical examples are illustrated and simulated to show the feasibility and
effectiveness of the proposed methods. |
| format | Article |
| id | doaj-art-061f24dde9d2425eacc4ed9f97a0412f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-061f24dde9d2425eacc4ed9f97a0412f2025-02-03T06:06:01ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/681523681523On Existence of Stabilizing Switching Laws within a Class of Unstable Linear SystemsSendren Sheng-Dong Xu0Chih-Chiang Chen1Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, Da’an District, Taipei 10607, TaiwanInstitute of Electrical Control Engineering, National Chiao Tung University, No. 1001, Ta Hsueh Road, Hsinchu 30010, TaiwanThe equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.http://dx.doi.org/10.1155/2013/681523 |
| spellingShingle | Sendren Sheng-Dong Xu Chih-Chiang Chen On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems Abstract and Applied Analysis |
| title | On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems |
| title_full | On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems |
| title_fullStr | On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems |
| title_full_unstemmed | On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems |
| title_short | On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems |
| title_sort | on existence of stabilizing switching laws within a class of unstable linear systems |
| url | http://dx.doi.org/10.1155/2013/681523 |
| work_keys_str_mv | AT sendrenshengdongxu onexistenceofstabilizingswitchinglawswithinaclassofunstablelinearsystems AT chihchiangchen onexistenceofstabilizingswitchinglawswithinaclassofunstablelinearsystems |