Input-to-output stability for infinite-dimensional systems
A question from SIAM Review (2020). Section 10.2; Definition 10.2; inspected PDF p. 70.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
Develop characterizations and Lyapunov methods for infinite-dimensional systems with output satisfying
where and . The research programme concerns general output maps and Banach-space states, beyond the delay-system and small-gain cases surveyed.
Lean 4
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Background
Editorial summary of Section 10.2; Definition 10.2; inspected PDF p. 70 in Input-to-state stability of infinite-dimensional systems: recent results and open questions. Read the original for the full definitions and context.
SIAM Review 62 (2020), 529–614. These are research programmes from §10, not single yes/no conjectures. The older Dirichlet heat Lyapunov question is not extracted because later work addresses it.
Progress & source assessment
The source presents this question or research direction as unresolved at the time of writing. Current status has not been independently established. Source inspected on 2026-09-10; this date is a provenance check, not certification that the question remains open.
- [1]Andrii Mironchenko, Christophe Prieur. Input-to-state stability of infinite-dimensional systems: recent results and open questions. SIAM Review (2020). linkSection 10.2; Definition 10.2; inspected PDF p. 70
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