Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909000658845696 |
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| author | Flavio, Picchiotti Lima, Thiago Alves Antoine, Girard |
| author_facet | Flavio, Picchiotti Lima, Thiago Alves Antoine, Girard |
| contents | In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps, independently of the switching sequence. We address both the mode-dependent case, where the controller has access to the active mode, and the mode-independent case, where a common feedback law must be employed. For each setting, we present constructive procedures to compute the stabilizing state-feedback gains. Building on these results, we then introduce a structural decomposition of switched systems, which serves to simplify stabilizability analysis and controller design. This allows us to establish the equivalence between fixed-time stabilizability and arbitrarily fast exponential stabilizability. The effectiveness of the proposed methods is illustrated through a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26455 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems Flavio, Picchiotti Lima, Thiago Alves Antoine, Girard Optimization and Control In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps, independently of the switching sequence. We address both the mode-dependent case, where the controller has access to the active mode, and the mode-independent case, where a common feedback law must be employed. For each setting, we present constructive procedures to compute the stabilizing state-feedback gains. Building on these results, we then introduce a structural decomposition of switched systems, which serves to simplify stabilizability analysis and controller design. This allows us to establish the equivalence between fixed-time stabilizability and arbitrarily fast exponential stabilizability. The effectiveness of the proposed methods is illustrated through a numerical example. |
| title | Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.26455 |