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Stability robustness of linear quadratic regulators
Author(s) -
Chen Ci,
Holohan Anthony
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3362
Subject(s) - weighting , robustness (evolution) , control theory (sociology) , diagonal , mathematics , singular value , quadratic equation , robust control , multivariable calculus , linear quadratic regulator , mathematical optimization , optimal control , computer science , control system , control (management) , engineering , control engineering , biochemistry , geometry , gene , artificial intelligence , chemistry , quantum mechanics , radiology , medicine , eigenvalues and eigenvectors , physics , electrical engineering
Summary In quadratic optimal control theory, the multivariable linear quadratic regulator is guaranteed to have excellent stability margins if the weight on the control inputs is diagonal. However, for the non‐diagonal case, it may suffer from poor robustness. In this paper, these robustness properties are studied in relation to weight selection. For general weighting matrices, a new lower bound on the minimum singular value of the return difference is presented. New guaranteed stability margins are also presented. This gives a formal mathematical basis for guidelines for weight selection. Copyright © 2015 John Wiley & Sons, Ltd.