Feedback rectifiable pairs and stabilization of switched linear systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918306141700096 |
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| author | Honecker, Maria C. Gernandt, Hannes Wulff, Kai Trunk, Carsten Reger, Johann |
| author_facet | Honecker, Maria C. Gernandt, Hannes Wulff, Kai Trunk, Carsten Reger, Johann |
| contents | We address the feedback design problem for switched linear systems. In particular we aim to design a switched state-feedback such that the resulting closed-loop subsystems share the same eigenstructure. To this effect we formulate and analyse the feedback rectification problem for pairs of matrices. We present necessary and sufficient conditions for the feedback rectifiability of pairs for two subsystems and give a constructive procedure to design stabilizing state-feedback for a class of switched systems. In particular the proposed algorithm provides sets of eigenvalues and corresponding eigenvectors for the closed-loop subsystems that guarantee stability for arbitrary switching. Several examples illustrate the characteristics of the problem considered and the application of the proposed design procedure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10591 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Feedback rectifiable pairs and stabilization of switched linear systems Honecker, Maria C. Gernandt, Hannes Wulff, Kai Trunk, Carsten Reger, Johann Optimization and Control Dynamical Systems 93D15, 93C30, 93B52, 93B55 We address the feedback design problem for switched linear systems. In particular we aim to design a switched state-feedback such that the resulting closed-loop subsystems share the same eigenstructure. To this effect we formulate and analyse the feedback rectification problem for pairs of matrices. We present necessary and sufficient conditions for the feedback rectifiability of pairs for two subsystems and give a constructive procedure to design stabilizing state-feedback for a class of switched systems. In particular the proposed algorithm provides sets of eigenvalues and corresponding eigenvectors for the closed-loop subsystems that guarantee stability for arbitrary switching. Several examples illustrate the characteristics of the problem considered and the application of the proposed design procedure. |
| title | Feedback rectifiable pairs and stabilization of switched linear systems |
| topic | Optimization and Control Dynamical Systems 93D15, 93C30, 93B52, 93B55 |
| url | https://arxiv.org/abs/2308.10591 |