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Pole assignment for linear and quadratic systems with time‐delay in control
Author(s) -
Li T.,
Chu E. KW.
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.817
Subject(s) - eigenvalues and eigenvectors , mathematics , linear subspace , quadratic equation , robustness (evolution) , lti system theory , linear system , invariant (physics) , simple (philosophy) , control theory (sociology) , control (management) , mathematical analysis , pure mathematics , computer science , geometry , biochemistry , chemistry , physics , philosophy , epistemology , quantum mechanics , artificial intelligence , mathematical physics , gene
SUMMARY We consider the pole assignment problems for time‐invariant linear and quadratic control systems, with time‐delay in the control. Closed‐loop eigenvectors in X = [ x 1 , x 2 , ⋯ ] are chosen from their corresponding invariant subspaces, possibly optimizing some robustness measure, and explicit expressions for the feedback matrices are given in terms of X . Condition of the problems is also investigated. Our approach extends the well‐known Kautsky, Nichols, and Van Dooren algorithm. Consequently, the results are similar to those for systems without time‐delay, except for the presence of the ‘secondary’ eigenvalues and the condition of the problems. Simple illustrative numerical examples are given. Copyright © 2011 John Wiley & Sons, Ltd.