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Robust H ∞ control of linear time‐varying systems with mixed delays in the Hilbert space
Author(s) -
Bay Nguyen S.,
Linh Nguyen M.,
Phat Vu N.
Publication year - 2010
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.952
Subject(s) - controllability , hilbert space , linear system , control theory (sociology) , mathematics , riccati equation , class (philosophy) , discrete time and continuous time , control (management) , differential equation , computer science , mathematical analysis , statistics , artificial intelligence
In this paper, a class of linear infinite‐dimensional systems with discrete and distributed time‐varying delays is studied. New sufficient conditions for the robust H ∞ control of linear time‐varying control systems with mixed time‐varying delays in Hilbert spaces have been established. The conditions are given in terms of the solution of a Riccati differential equation. Furthermore, it is proved for the first time that the solution to the robust H ∞ control problem can be solved by the global controllability of an appropriate linear control delay‐like system. Copyright © 2010 John Wiley & Sons, Ltd.