On the use of the generalized structured singular value for decentralized control problems

Author

Tanaka, Takashi ; Langbort, Cédric

Author_Institution

Dept. of Aerosp. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

1632

Lastpage

1637

Abstract

We study how the maximum/minimum gain of a decentralized controller influences the maximum/minimum gain of the corresponding closed loop transfer function, and provide lower bounds on the best closed-loop performance achievable by decentralized controllers satisfying additional frequency domain restrictions. These bounds are obtained using generalizations of the structured singular value and approximated by the solution of linear matrix inequalities (LMI). We close by applying our results to an active sound control problem.

Keywords

closed loop systems; decentralised control; linear matrix inequalities; singular value decomposition; transfer functions; closed loop transfer function; decentralized controller; frequency domain restriction; generalized structured singular value; linear matrix inequalities; maximum gain; minimum gain; Control engineering education; Design methodology; Distributed control; Frequency domain analysis; Linear matrix inequalities; Lyapunov method; Optimal control; Performance analysis; Performance gain; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400171

Filename

5400171