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A comparison of some robust eigenvalue assignment techniques
Author(s) -
Burrows Simon P.,
Patton Ron J.
Publication year - 1990
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660110406
Subject(s) - eigenvalues and eigenvectors , linear subspace , mathematics , algorithm , matrix (chemical analysis) , orthographic projection , projection (relational algebra) , eigenvalue perturbation , inverse iteration , generalized eigenvector , eigendecomposition of a matrix , iterative method , mathematical optimization , computer science , symmetric matrix , pure mathematics , state transition matrix , geometry , physics , materials science , quantum mechanics , composite material
Three techniques for robust eigenvalue assignment are presented. The first is well known and is based on iteratively assigning the closed‐loop eigenvectors so as to be maximally orthogonal to one another. The second has been recently presented by the authors and is an improvement of the first which gives better results for problems where complex‐conjugate eigenvalue pairs are to be assigned. The final method is new and is founded on the iterative replacement of the current closed‐loop eigenvector matrix with a new matrix which is the projection of the columns of the nearest orthogonal matrix into the allowable eigenvector subspaces. Some numerical examples are given which are used to illustrate the improved results obtained using the second technique in place of the first and to compare these with the performance of the last algorithm which is based on an alternative approach.