Input-to-state stability in integral norms for linear infinite-dimensional systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914593023983616 |
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| author | Arora, Sahiba Mironchenko, Andrii |
| author_facet | Arora, Sahiba Mironchenko, Andrii |
| contents | We study integral-to-integral input-to-state stability for infinite-dimensional linear systems with inputs and trajectories in $L^p$-spaces.
We start by developing the corresponding admissibility theory for linear systems with unbounded input operators.
While input-to-state stability is typically characterised by exponential stability and finite-time admissibility, we show that this equivalence does not extend directly to integral norms. For analytic semigroups, we establish a precise characterisation using maximal regularity theory. Additionally, we provide direct Lyapunov theorems and construct Lyapunov functions for $L^p$-$L^q$-ISS and demonstrate the results with examples, including diagonal systems and diffusion equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Input-to-state stability in integral norms for linear infinite-dimensional systems Arora, Sahiba Mironchenko, Andrii Optimization and Control Functional Analysis 93C25, 37B25, 93D09, 93D20, 93C20, 37C75 We study integral-to-integral input-to-state stability for infinite-dimensional linear systems with inputs and trajectories in $L^p$-spaces. We start by developing the corresponding admissibility theory for linear systems with unbounded input operators. While input-to-state stability is typically characterised by exponential stability and finite-time admissibility, we show that this equivalence does not extend directly to integral norms. For analytic semigroups, we establish a precise characterisation using maximal regularity theory. Additionally, we provide direct Lyapunov theorems and construct Lyapunov functions for $L^p$-$L^q$-ISS and demonstrate the results with examples, including diagonal systems and diffusion equations. |
| title | Input-to-state stability in integral norms for linear infinite-dimensional systems |
| topic | Optimization and Control Functional Analysis 93C25, 37B25, 93D09, 93D20, 93C20, 37C75 |
| url | https://arxiv.org/abs/2501.07680 |