Stability under dwell time constraints: Discretization revisited
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917584377479168 |
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| author | Mejstrik, Thomas Protasov, Vladimir Yu. |
| author_facet | Mejstrik, Thomas Protasov, Vladimir Yu. |
| contents | We decide the stability and compute the Lyapunov exponent of continuous-time linear switching systems with a guaranteed dwell time. The main result asserts that the discretization method with step size~$h$ approximates the Lyapunov exponent with the precision~$C\,h^2$, where~$C$ is a constant. Let us stress that without the dwell time assumption, the approximation rate is known to be linear in~$h$. Moreover, for every system, the constant~$C$ can be explicitly evaluated. In turn, the discretized system can be treated by computing the Markovian joint spectral radius of a certain system on a graph. This gives the value of the Lyapunov exponent with a high accuracy. The method is efficient for dimensions up to, approximately, ten; for positive systems, the dimensions can be much higher, up to several hundreds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability under dwell time constraints: Discretization revisited Mejstrik, Thomas Protasov, Vladimir Yu. Dynamical Systems 49M25, 93C30, 37C20, 15A60 We decide the stability and compute the Lyapunov exponent of continuous-time linear switching systems with a guaranteed dwell time. The main result asserts that the discretization method with step size~$h$ approximates the Lyapunov exponent with the precision~$C\,h^2$, where~$C$ is a constant. Let us stress that without the dwell time assumption, the approximation rate is known to be linear in~$h$. Moreover, for every system, the constant~$C$ can be explicitly evaluated. In turn, the discretized system can be treated by computing the Markovian joint spectral radius of a certain system on a graph. This gives the value of the Lyapunov exponent with a high accuracy. The method is efficient for dimensions up to, approximately, ten; for positive systems, the dimensions can be much higher, up to several hundreds. |
| title | Stability under dwell time constraints: Discretization revisited |
| topic | Dynamical Systems 49M25, 93C30, 37C20, 15A60 |
| url | https://arxiv.org/abs/2402.04795 |