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Sufficient conditions for admissibility. (English) Zbl 1129.93422

Summary: Sufficient conditions for the finite and infinite-time admissibility of an observation operator are given. It is shown that the estimates of Weiss are close to being sufficient. If the semigroup is surjective, then the estimate is sufficient.

MSC:

93C25 Control/observation systems in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
47N70 Applications of operator theory in systems, signals, circuits, and control theory
93B05 Controllability

References:

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[5] Partington, J. R.; Weiss, G., Admissible observation operators for the right shift semigroup, Math. Control Syst. Signal., 13, 179-192 (2000) · Zbl 0966.93033
[6] Weiss, G., Admissible observation operators for linear semigroups, Israel J. Math., 65, 17-43 (1989) · Zbl 0696.47040
[7] Weiss, G., Two conjectures on the admissibility of control operators, (Kappel, F.; Desch, W., Estimation and Control of Distributed Parameter Systems (1991), Birkhäuser Verlag: Birkhäuser Verlag Basel), 367-378 · Zbl 0763.93041
[8] Weiss, G., A powerful generalization of the Carleson measure theorem, (Blondel, V.; Sontag, E.; Vidyasagar, M.; Willems, J., Open Problems in Mathematical Systems Theory and Control (1998), Springer: Springer Berlin), 267-272
[9] Zwart, H.; Jacob, B.; Staffans, O., Weak admissibility does not imply admissibility for analytic semigroups, Syst. Control Lett., 48, 341-350 (2003) · Zbl 1157.93421
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