Sparse Representations of Dynamical Networks: A Coprime Factorization Approach
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915645725081600 |
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| author | Sabău, Şerban Sperilă, Andrei Oară, Cristian Jadbabaie, Ali |
| author_facet | Sabău, Şerban Sperilă, Andrei Oară, Cristian Jadbabaie, Ali |
| contents | We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the structure of their component subsystems' interconnection. In doing so, we provide tractable means of shifting between different types of sparsity-preserving representations and we show how to employ these factorizations to obtain distributed implementations for stabilizing and possibly stable controllers. By formulating all these results for both discrete- and continuous-time systems, we develop specialized distributed implementations that, up to this point, were only available for networks modeled as discrete-time systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2206_09945 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sparse Representations of Dynamical Networks: A Coprime Factorization Approach Sabău, Şerban Sperilă, Andrei Oară, Cristian Jadbabaie, Ali Systems and Control 93A14, 93B99, 93C05 We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the structure of their component subsystems' interconnection. In doing so, we provide tractable means of shifting between different types of sparsity-preserving representations and we show how to employ these factorizations to obtain distributed implementations for stabilizing and possibly stable controllers. By formulating all these results for both discrete- and continuous-time systems, we develop specialized distributed implementations that, up to this point, were only available for networks modeled as discrete-time systems. |
| title | Sparse Representations of Dynamical Networks: A Coprime Factorization Approach |
| topic | Systems and Control 93A14, 93B99, 93C05 |
| url | https://arxiv.org/abs/2206.09945 |