×

Disturbance decoupling by measurement feedback with stability for infinite-dimensional systems. (English) Zbl 0591.93032

This paper uses a geometric approach for the system design of infinite- dimensional systems. The author extends the concepts of controllability and stabilizability subspaces to infinite-dimensional linear systems. Under certain assumptions she obtains a generalization of the finite- dimensional theory. By dualizing she also derives similar results for the concepts of complementary observability and complementary detectability subspaces. She uses these concepts to solve the infinite-dimensional version of the disturbance-decoupling problem, the disturbance-decoupled estimation problem and the disturbance-decoupling problem with measurement feedback. The solution is in terms of geometric concepts such as (A,B)- and (C,A)-invariant subspaces and controllability and complementary observability subspaces.
Reviewer: T.Kobayashi

MSC:

93C25 Control/observation systems in abstract spaces
47A15 Invariant subspaces of linear operators
93C05 Linear systems in control theory
93B05 Controllability
93B07 Observability
93D15 Stabilization of systems by feedback
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1109/TAC.1982.1102875 · Zbl 0477.93039 · doi:10.1109/TAC.1982.1102875
[2] DOI: 10.1007/BFb0006761 · doi:10.1007/BFb0006761
[3] KATO T., Perturbation Theory for Linear Operators (1966) · Zbl 0148.12601
[4] DOI: 10.1007/BF01442887 · Zbl 0478.93027 · doi:10.1007/BF01442887
[5] SCHUMACHER , J. M. , 1982 , Dynamic feedback in finite and infinite-dimensional linear systems , M. C. Tract No. 143, Mathematisch Centrum , Amsterdam .
[6] TAYLOR A. E., Introduction to Functional Analysis (1980) · Zbl 0501.46003
[7] DOI: 10.1137/0319029 · Zbl 0467.93036 · doi:10.1137/0319029
[8] WONHAM W. H., Linear Multivariable Control A Geometric Approach (1979) · Zbl 0424.93001
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.