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arXiv · 2501.07680

Input-to-state stability in integral norms for linear infinite-dimensional systems

Sahiba Arora·Andrii Mironchenko
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Abstract

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.

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Sahiba Arora, Andrii Mironchenko. 2025-01-13. Input-to-state stability in integral norms for linear infinite-dimensional systems. https://arxiv.org/abs/2501.07680

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