84 research outputs found

    Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

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    The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the versal deformation theory for matrices. Numerical examples are given. The implementation of the method in MATLAB code is available.Comment: 19 pages, 3 figure

    Reduced order feedback control equations for linear time and frequency domain analysis

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    An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized

    The Weyr Characteristic

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    On the numerical solution of the discrete time algebraic Riccati equation

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    Bibliography: leaf 38."May 1979."Contract ERDA-E(49-18)-2087 Contract No. DAAG29-79-C-0031by T. Pappas, A.J. Laub, N.R. Sandell, Jr

    Linear multivariable control : numerical considerations

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    Bibliography: p. 31-32.Grant ERDA-E(49-18)-2087.by Alan J. Laub

    Calculation of transmission zeros using QZ techniques

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    Bibliography: leaves 23-25.Contract ERDA-E(49-18)-2087.by A. J. Laub and B. C. Moore
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