Passive and reciprocal linear time-and-space-invariant systems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914147362406400 |
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| author | Shali, Brayan M. Sepulchre, Rodolphe |
| author_facet | Shali, Brayan M. Sepulchre, Rodolphe |
| contents | Reciprocity is a fundamental symmetry property observed across many physical domains, including acoustics, elasticity, electromagnetics, and thermodynamics. In systems and control theory, it provides key insights into the internal structure of linear time-invariant (LTI) systems and is closely linked to properties such as passivity, relaxation, and time-reversibility. This paper extends the concept of reciprocity to linear time-and-space-invariant (LTSI) systems, a class of infinite-dimensional systems with spatio-temporal dynamics. It is suggested that, analogously to the LTI case, combining the internal properties of reciprocity and (impedance) passivity entails physical state-space realizations. This is of particular relevance for infinite-dimensional systems, where issues of unboundedness can be detrimental to the well-posedness of the system. The results are motivated and illustrated with a physical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Passive and reciprocal linear time-and-space-invariant systems Shali, Brayan M. Sepulchre, Rodolphe Optimization and Control Reciprocity is a fundamental symmetry property observed across many physical domains, including acoustics, elasticity, electromagnetics, and thermodynamics. In systems and control theory, it provides key insights into the internal structure of linear time-invariant (LTI) systems and is closely linked to properties such as passivity, relaxation, and time-reversibility. This paper extends the concept of reciprocity to linear time-and-space-invariant (LTSI) systems, a class of infinite-dimensional systems with spatio-temporal dynamics. It is suggested that, analogously to the LTI case, combining the internal properties of reciprocity and (impedance) passivity entails physical state-space realizations. This is of particular relevance for infinite-dimensional systems, where issues of unboundedness can be detrimental to the well-posedness of the system. The results are motivated and illustrated with a physical example. |
| title | Passive and reciprocal linear time-and-space-invariant systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.07258 |