On maximal positive invariant set computation for rank-deficient linear systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911525730516992 |
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| author | Gheorghe, Bogdan Ioan, Daniel Flutur, Cristian Prodan, Ionela Stoican, Florin |
| author_facet | Gheorghe, Bogdan Ioan, Daniel Flutur, Cristian Prodan, Ionela Stoican, Florin |
| contents | The maximal positively invariant (MPI) set is obtained through a backward reachability procedure involving the iterative computation and intersection of predecessor sets under state and input constraints.
However, standard static feedback synthesis may place some of the closed-loop eigenvalues at zero, leading to rank-deficient dynamics. This affects the MPI computation by inducing projections onto lower-dimensional subspaces during intermediate steps. By exploiting the Schur decomposition, we explicitly address this singular case and propose a robust algorithm that computes the MPI set in both polyhedral and constrained-zonotope representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On maximal positive invariant set computation for rank-deficient linear systems Gheorghe, Bogdan Ioan, Daniel Flutur, Cristian Prodan, Ionela Stoican, Florin Systems and Control Optimization and Control The maximal positively invariant (MPI) set is obtained through a backward reachability procedure involving the iterative computation and intersection of predecessor sets under state and input constraints. However, standard static feedback synthesis may place some of the closed-loop eigenvalues at zero, leading to rank-deficient dynamics. This affects the MPI computation by inducing projections onto lower-dimensional subspaces during intermediate steps. By exploiting the Schur decomposition, we explicitly address this singular case and propose a robust algorithm that computes the MPI set in both polyhedral and constrained-zonotope representations. |
| title | On maximal positive invariant set computation for rank-deficient linear systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2603.17686 |