×

zbMATH — the first resource for mathematics

Admissibility of observation functionals. (English) Zbl 0837.93005
The concept of infinite-time admissibility of unbounded observation functionals is introduced. Under the assumption of exponential stability of the semigroup, it is equivalent to finite-time admissibility recently investigated by Weiss. Necessary and sufficient criteria for admissibility are given. In particular, it is shown that the Ho-Russell- Weiss test for admissibility of observation functionals/control vectors can be derived in an elementary way without invoking the geometric interpretation of the Carleson measure, while the criterion by Weiss can easily be deduced from the Carleson embedding theorem. Some practically applicable sufficient conditions guaranteeing admissibility are discussed in Section 3. The results are illustrated by a feedback system containing an RLCG transmission line.

MSC:
93B07 Observability
93C25 Control/observation systems in abstract spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1090/S0002-9947-1988-0933321-3
[2] BARI N. K., Utchebnye Zapiski MGU 4 pp 69– (1951)
[3] DOI: 10.1090/S0273-0979-1990-15894-X · Zbl 0727.47001
[4] FATTORINI H. O., Second Order Linear Differential Equations in Banach Spaces (1985) · Zbl 0564.34063
[5] FUHRMANN P., Linear Systems and Operators in Hilbert Space (1981) · Zbl 0456.47001
[6] DOI: 10.1093/imamci/7.4.317 · Zbl 0721.49006
[7] KATSNEL’SON V. E., Funktsional’nyi Analiz i ego Prilozheniya 1 pp 39– (1967)
[8] LYUBICH YU., Studia Mathematica 88 pp 37– (1988)
[9] NIKOL’SKII N. K., Treatise on the Shift Operator (1985)
[10] PAZY A., Semigroups of Linear Operators and Applications to PDEs (1983) · Zbl 0516.47023
[11] SHKALIKOV A. A., Uspekhi Mat. Nauk. 34 pp 235– (1979)
[12] DOI: 10.1016/0022-0396(88)90075-7 · Zbl 0675.47031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.