Use of reduced forms in the disturbance decoupling problem

Specific algorithms, such as those involving the supremal of the invariant subspaces contained in a suitable subspace, are known to be able to test whether a Disturbance Decoupling Problem (DDP) is solvable. Here, by reducing the system to its Molinari form, we obtain an alternative description of t...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 430; no. 5; pp. 1574 - 1589
Main Authors: Compta, Albert, Ferrer, Josep, Peña, Marta
Format: Journal Article Conference Proceeding Publication
Language:English
Published: Amsterdam Elsevier Inc 01.03.2009
Elsevier
Subjects:
93 Systems Theory; Control
93B Controllability, observability, and system structure
93C Control systems, guided systems
[formula omitted]-Invariant subspaces
Algebra
Classificació AMS
Controllability subspaces
Disturbance decoupling problem
Exact sciences and technology
Invariant subspaces
Linear and multilinear algebra, matrix theory
Matemàtiques i estadística
Mathematics
Molinari reduced form
Sciences and techniques of general use
Àrees temàtiques de la UPC
( A , B ) -Invariant subspaces
Disturbance decoupling problem
Controllability subspaces
93B27
93C73
Molinari reduced form
Closed loop
Closed systems
Invariant subspace
Vector space
Feedback regulation
Controllability
93B27; 93C73; Disturbance decoupling problem; (A
Solvability
B)-Invariant subspaces; Controllability subspaces; Molinari reduced form
ISSN:0024-3795
Online Access:Get full text
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Summary:Specific algorithms, such as those involving the supremal of the invariant subspaces contained in a suitable subspace, are known to be able to test whether a Disturbance Decoupling Problem (DDP) is solvable. Here, by reducing the system to its Molinari form, we obtain an alternative description of this supremal object and compute its dimension. Hence we have a general result for solving the decoupling provided that a Molinari basis is known. In particular, a necessary numerical condition for it is derived. The same technique is applied to the DDPS, that is, when stability of the decoupled closed loop system is required.
ISSN:0024-3795
DOI:10.1016/j.laa.2008.04.033