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  • 1
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    An efficient algorithm for calculation of the Luenberger canonical form (1972)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: An algorithm is suggested to obtain the Luenberger canonical form for multivariable systems. The method computes the canonical form directly without having to compute the transformation matrix. In addition, there is a large reduction in the number of calculations. The reduced computations along with Gaussian techniques lend to greater inherent accuracy and the ability to refine the solution with additional computations.
    Keywords: MATHEMATICS
    Type: NASA-CR-129174 , TR-72-9
    Format: application/pdf
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  • 2
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    Decoupling and pole placement via transfer matrix synthesis (1971)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Decoupling and pole placement via transfer matrix synthesis
    Keywords: MATHEMATICS
    Type: NASA-CR-123163
    Format: application/pdf
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  • 3
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    An efficient algorithm for calculation of the Luenberger canonical form. (1973)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.
    Keywords: MATHEMATICS
    Type: IEEE Transactions on Automatic Control; AC-18; June 197
    Format: text
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  • 4
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    An algorithm for calculation of the Jordan canonical form of a matrix (1973)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.
    Keywords: MATHEMATICS
    Type: NASA-CR-131654 , TR-73-1
    Format: application/pdf
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  • 5
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    On the use and computation of the Jordan canonical form in system theory (1974)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.
    Keywords: MATHEMATICS
    Type: Asilomar Conference on Circuits, Systems, and Computers; Nov 27, 1973 - Nov 29, 1973; Pacific Grove, CA
    Format: text
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