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Minimum Norm Regularization of Descriptor Systems by Output FeedbackChu, D., Mehrmann, V. 30 October 1998 (has links) (PDF)
We study the regularization problem for linear, constant coefficient descriptor
systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative
mixed output feedback. Necessary and sufficient conditions are given, which guarantee
that there exist output feedbacks such that the closed-loop system is regular, has
index at most one and $E +BG\Gamma$ has
a desired rank, i.e. there is a desired number of differential and algebraic equations.
To resolve the freedom in the choice of the feedback matrices we then discuss how
to obtain the desired regularizing feedback of minimum norm and show that this approach
leads to useful results in the sense of robustness only if the rank of E is
decreased. Numerical procedures are derived to construct the desired feedbacks gains.
These numerical procedures are based on orthogonal matrix transformations which
can be implemented in a numerically stable way.
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A parallel version of the preconditioned conjugate gradient method for boundary element equationsPester, M., Rjasanow, S. 30 October 1998 (has links) (PDF)
The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
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A parallel preconditioned iterative realization of the panel method in 3DPester, M., Rjasanow, S. 30 October 1998 (has links) (PDF)
The parallel version of precondition iterative techniques is
developed for matrices arising from the panel boundary element
method for three-dimensional simple connected domains with
Dirichlet boundary conditions. Results were obtained on an
nCUBE-2 parallel computer showing that iterative solution methods
are very well suited also in three-dimensional case for
implementation on a MIMD computer and that they are much more
efficient than usual direct solution techniques.
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A parallel preconditioned iterative realization of the panel method in 3DPester, M., Rjasanow, S. 30 October 1998 (has links)
The parallel version of precondition iterative techniques is
developed for matrices arising from the panel boundary element
method for three-dimensional simple connected domains with
Dirichlet boundary conditions. Results were obtained on an
nCUBE-2 parallel computer showing that iterative solution methods
are very well suited also in three-dimensional case for
implementation on a MIMD computer and that they are much more
efficient than usual direct solution techniques.
|
5 |
Minimum Norm Regularization of Descriptor Systems by Output FeedbackChu, D., Mehrmann, V. 30 October 1998 (has links)
We study the regularization problem for linear, constant coefficient descriptor
systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative
mixed output feedback. Necessary and sufficient conditions are given, which guarantee
that there exist output feedbacks such that the closed-loop system is regular, has
index at most one and $E +BG\Gamma$ has
a desired rank, i.e. there is a desired number of differential and algebraic equations.
To resolve the freedom in the choice of the feedback matrices we then discuss how
to obtain the desired regularizing feedback of minimum norm and show that this approach
leads to useful results in the sense of robustness only if the rank of E is
decreased. Numerical procedures are derived to construct the desired feedbacks gains.
These numerical procedures are based on orthogonal matrix transformations which
can be implemented in a numerically stable way.
|
6 |
A parallel version of the preconditioned conjugate gradient method for boundary element equationsPester, M., Rjasanow, S. 30 October 1998 (has links)
The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
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