Reachability Analysis of the State Transition and State Covariance Matrices for an LTV System
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913065993240576 |
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| author | Liu, Fengjiao Zhang, Yixiao Tsiotras, Panagiotis |
| author_facet | Liu, Fengjiao Zhang, Yixiao Tsiotras, Panagiotis |
| contents | In this paper, we study the reachability of two closely related matrices appearing in the analysis of linear time-varying (LTV) systems over a finite time interval, namely, its closed-loop state transition matrix via a state feedback control and its state covariance matrix starting from some given initial state covariance matrix. Under a mild assumption, we first characterize the set of closed-loop terminal state transition matrices reachable from the identity matrix using controls of the state feedback form. Then, we provide the set of terminal state covariance matrices reachable from any given positive definite initial state covariance matrix when the LTV system is not necessarily controllable. Both results are based on the solutions of corresponding matrix Riccati differential equations (RDE). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reachability Analysis of the State Transition and State Covariance Matrices for an LTV System Liu, Fengjiao Zhang, Yixiao Tsiotras, Panagiotis Systems and Control In this paper, we study the reachability of two closely related matrices appearing in the analysis of linear time-varying (LTV) systems over a finite time interval, namely, its closed-loop state transition matrix via a state feedback control and its state covariance matrix starting from some given initial state covariance matrix. Under a mild assumption, we first characterize the set of closed-loop terminal state transition matrices reachable from the identity matrix using controls of the state feedback form. Then, we provide the set of terminal state covariance matrices reachable from any given positive definite initial state covariance matrix when the LTV system is not necessarily controllable. Both results are based on the solutions of corresponding matrix Riccati differential equations (RDE). |
| title | Reachability Analysis of the State Transition and State Covariance Matrices for an LTV System |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.24691 |