Higher Dimensional Feedback Stabilization by Sampling

Definitions and mathematical statement

Requested extension. Extend the data-rate or sampling procedures for feedback stabilization described in the cited report from the setting with two unstable eigenvalues to higher-dimensional systems, preserving the stabilization guarantees of those procedures.

Definitions and unresolved qualifications. A precise formulation requires specifying the dynamical systems under consideration, their state spaces, the admissible observations and control inputs, the sampling or communication constraints, and the meaning of stabilization. The expression "unstable eigenvalue" also requires an identified operator and a stability criterion; neither is supplied. The record does not specify whether eigenvalues are counted with algebraic or geometric multiplicity.

The supplied original statement includes both data-rate and sampling procedures, whereas the supplied cleaned statement mentions only sampling-based procedures. Both possibilities are retained here pending identification of the intended construction. Moreover, "higher-dimensional" does not determine whether the proposed extension concerns larger state-space dimension, more than two unstable eigenvalues, or both. No precise stabilization property, quantitative bound, admissible system class, or baseline procedure is supplied. Consequently, the requested extension above is a statement of the research objective; the supplied evidence does not determine a fully quantified mathematical conjecture or a precise theorem to be established.

Short English statement

Generalize the cited feedback-stabilization procedures beyond their setting with two unstable eigenvalues while retaining their guarantees. The system class, sampling or data-rate restrictions, meaning of higher dimension, and stabilization guarantees must be recovered from the source before a precise mathematical statement can be completed.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30003745$, source problem code catalogue entry, title Higher Dimensional Feedback Stabilization by Sampling, in the Oberwolfach Reports Open Problems collection. Local registry locations identified by the project are data/unsolvedmath/problems.json and catalog/problems.json; no independent inspection of these files is asserted.
• Supplied source citation: Mini-Workshop: Entropy, Information and Control (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/10, pp. 531--558. Supplied source URL: https://doi.org/10.4171/owr/2018/10. The record gives proposed year 2018 and names no individual proposer. The relationship between the citation's year 2019 and its 2018 DOI and proposed year is unresolved.
• Supplied literature reference: Oberwolfach Report 10, https://doi.org/10.4171/OWR/2018/10.
• Supplied literature reference: Event-based Containability, https://www.sciencedirect.com/science/article/pii/S2405896319319858. No authors or precise supporting passage are supplied.
• Literature assessment checked at 2026-08-21: the supplied curation labels the problem open and reports that the construction with two unstable eigenvalues is established, while the stated higher-dimensional generalization remains unresolved in the primary report and subsequent work. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The source explicitly requests independent verification of time-sensitive status and cited claims.