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...
Uložené v:
| Vydané v: | Linear & multilinear algebra Ročník 72; číslo 4; s. 655 - 677 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Abingdon
Taylor & Francis
03.03.2024
Taylor & Francis Ltd |
| Predmet: | |
| ISSN: | 0308-1087, 1563-5139 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | 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). |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0308-1087 1563-5139 |
| DOI: | 10.1080/03081087.2022.2160945 |