84 research outputs found
Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters
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
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
On the numerical solution of the discrete time algebraic Riccati equation
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
Bibliography: p. 31-32.Grant ERDA-E(49-18)-2087.by Alan J. Laub
Calculation of transmission zeros using QZ techniques
Bibliography: leaves 23-25.Contract ERDA-E(49-18)-2087.by A. J. Laub and B. C. Moore
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