Exponential stability of switched block triangular systems under arbitrary switching
In this paper, exponential stability of continuous-time and discrete-time switched $ k\times k $ k × k block triangular systems under arbitrary switching is studied. Firstly, under the assumption that all subsystem matrices are Hurwitz and a family of those corresponding block diagonal matrices is c...
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| Vydáno v: | Linear & multilinear algebra Ročník 72; číslo 4; s. 655 - 677 |
|---|---|
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Abingdon
Taylor & Francis
03.03.2024
Taylor & Francis Ltd |
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| ISSN: | 0308-1087, 1563-5139 |
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| Abstract | In this paper, exponential stability of continuous-time and discrete-time switched
$ k\times k $
k
×
k
block triangular systems under arbitrary switching is studied. Firstly, under the assumption that all subsystem matrices are Hurwitz and a family of those corresponding block diagonal matrices is commutative, we prove that a continuous-time switched linear system is exponentially stable under arbitrary switching. Next, under the assumption that all subsystem matrices are Hurwitz and all those block diagonal matrices are normal, it is shown that the same switched system is exponentially stable under arbitrary switching. Further, under similar conditions we prove that a discrete-time switched linear system is exponentially stable under arbitrary switching. After that, illustrative numerical examples of the obtained results are also given. Finally, we prove that
$ 3\times 3 $
3
×
3
normal matrices have nine parameter representations which are useful for numerical examples (in the Appendix). |
|---|---|
| AbstractList | In this paper, exponential stability of continuous-time and discrete-time switched
$ k\times k $
k
×
k
block triangular systems under arbitrary switching is studied. Firstly, under the assumption that all subsystem matrices are Hurwitz and a family of those corresponding block diagonal matrices is commutative, we prove that a continuous-time switched linear system is exponentially stable under arbitrary switching. Next, under the assumption that all subsystem matrices are Hurwitz and all those block diagonal matrices are normal, it is shown that the same switched system is exponentially stable under arbitrary switching. Further, under similar conditions we prove that a discrete-time switched linear system is exponentially stable under arbitrary switching. After that, illustrative numerical examples of the obtained results are also given. Finally, we prove that
$ 3\times 3 $
3
×
3
normal matrices have nine parameter representations which are useful for numerical examples (in the Appendix). In this paper, exponential stability of continuous-time and discrete-time switched k×k block triangular systems under arbitrary switching is studied. Firstly, under the assumption that all subsystem matrices are Hurwitz and a family of those corresponding block diagonal matrices is commutative, we prove that a continuous-time switched linear system is exponentially stable under arbitrary switching. Next, under the assumption that all subsystem matrices are Hurwitz and all those block diagonal matrices are normal, it is shown that the same switched system is exponentially stable under arbitrary switching. Further, under similar conditions we prove that a discrete-time switched linear system is exponentially stable under arbitrary switching. After that, illustrative numerical examples of the obtained results are also given. Finally, we prove that 3×3 normal matrices have nine parameter representations which are useful for numerical examples (in the Appendix). |
| Author | Otsuka, Naohisa Shimizu, Tomoharu |
| Author_xml | – sequence: 1 givenname: Naohisa surname: Otsuka fullname: Otsuka, Naohisa email: otsuka@mail.dendai.ac.jp organization: Tokyo Denki University – sequence: 2 givenname: Tomoharu surname: Shimizu fullname: Shimizu, Tomoharu organization: Tokyo Denki University |
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| Cites_doi | 10.1016/j.na.2006.01.034 10.1109/9.362846 10.1016/j.mcm.2010.11.062 10.1016/j.aml.2009.03.023 10.1137/1.9781611970777 10.1007/1-84628-131-8 10.1007/978-0-85729-256-8 10.1016/0024-3795(87)90168-6 10.1016/S0167-6911(97)00004-2 10.1007/978-1-4612-0107-6 10.1109/9.754812 10.1016/0005-1098(91)90047-6 10.1016/S0167-6911(98)00082-6 10.1007/978-1-4612-0017-8 10.1016/j.na.2006.02.024 10.1016/j.nahs.2009.03.004 |
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| References | Matni N (e_1_3_3_16_1) 2011 Zhai G (e_1_3_3_19_1) 2014 Shorten RN (e_1_3_3_12_1) 1998 e_1_3_3_7_1 e_1_3_3_6_1 e_1_3_3_9_1 e_1_3_3_8_1 e_1_3_3_18_1 e_1_3_3_17_1 Mori Y (e_1_3_3_11_1) 1997 e_1_3_3_14_1 e_1_3_3_13_1 Lin H (e_1_3_3_4_1) 2014; 1 e_1_3_3_15_1 e_1_3_3_3_1 e_1_3_3_10_1 e_1_3_3_21_1 e_1_3_3_2_1 e_1_3_3_20_1 e_1_3_3_5_1 e_1_3_3_22_1 |
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| Snippet | In this paper, exponential stability of continuous-time and discrete-time switched
$ k\times k $
k
×
k
block triangular systems under arbitrary switching is... In this paper, exponential stability of continuous-time and discrete-time switched k×k block triangular systems under arbitrary switching is studied. Firstly,... |
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| SubjectTerms | arbitrary switching block triangular systems Continuous time systems Discrete time systems exponential stability Linear systems normal matrices Stability Subsystems Switched systems Switching |
| Title | Exponential stability of switched block triangular systems under arbitrary switching |
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