A Periodic Dichotomy in Linear Control Theory
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913006696267776 |
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| author | Ye, Shichao Zeng, Xingwu Zhang, Can |
| author_facet | Ye, Shichao Zeng, Xingwu Zhang, Can |
| contents | In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic linear quadratic optimal control problems. Specifically, we establish a complete characterization of the optimal extremal under suitable exponential stabilizability and detectability assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04003 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Periodic Dichotomy in Linear Control Theory Ye, Shichao Zeng, Xingwu Zhang, Can Optimization and Control In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic linear quadratic optimal control problems. Specifically, we establish a complete characterization of the optimal extremal under suitable exponential stabilizability and detectability assumptions. |
| title | A Periodic Dichotomy in Linear Control Theory |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.04003 |