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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Bibliographic Details
Published in:Linear & multilinear algebra Vol. 72; no. 4; pp. 655 - 677
Main Authors: Otsuka, Naohisa, Shimizu, Tomoharu
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.03.2024
Taylor & Francis Ltd
Subjects:
arbitrary switching
block triangular systems
Continuous time systems
Discrete time systems
exponential stability
Linear systems
normal matrices
Stability
Subsystems
Switched systems
Switching
ISSN:0308-1087, 1563-5139
Online Access:Get full text
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Summary: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).
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2022.2160945