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Robust eigenvalue assignment in second‐order systems: a gradient flow approach
Author(s) -
Chan H. C.,
Lam J.,
Ho D. W. C.
Publication year - 1997
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/(sici)1099-1514(199707/08)18:4<283::aid-oca603>3.0.co;2-q
Subject(s) - eigenvalues and eigenvectors , robustness (evolution) , mathematics , balanced flow , linear system , flow (mathematics) , mathematical optimization , control theory (sociology) , computer science , mathematical analysis , physics , geometry , biochemistry , chemistry , control (management) , quantum mechanics , artificial intelligence , gene
In this paper the problem of robust eigenvalue assignment in second‐order systems by combined derivative and proportional state feedback is examined. It is shown that almost arbitrary assignment can be achieved by solving a linear matrix equation or symmetric linear system. Based on the fact that the robustness of the spectrum is characterized by the condition number of the eigenvectors, an alternative objective function is defined and minimized by utilizing the gradient flow technique. Numerical tests are performed to illustrate the approach. © 1997 John Wiley & Sons, Ltd.