On limitations in H∞ suboptimal decentralized control derived from the generalized structured singular value

Takashi Tanaka; Cédric Langbort

doi:10.1016/j.sysconle.2011.02.005

On limitations in ^H∞ suboptimal decentralized control derived from the generalized structured singular value

Research output: Contribution to journal › Article › peer-review

Abstract

We study how the maximum/minimum gain of a decentralized or sparse controller over a frequency interval influences the maximum/minimum gain of the corresponding closed-loop transfer function over that interval. In doing so, we derive lower bounds on the best closed-loop performance achievable by decentralized and sparse controllers satisfying additional frequency domain restrictions, and sufficient conditions for a structured controller to guarantee a desired level of closed-loop performance. This results in graphical tests for the controller's singular value plots. These bounds are obtained by using tools inspired by generalizations of the structured singular value, and can be computed by solving Linear Matrix Inequalities (LMI). We close by applying our results to an active sound control problem.

Original language	English (US)
Pages (from-to)	318-324
Number of pages	7
Journal	Systems and Control Letters
Volume	60
Issue number	5
DOIs	https://doi.org/10.1016/j.sysconle.2011.02.005
State	Published - May 2011

Keywords

Decentralized and structured control
Generalized structured singular value
LMI
Robust control

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Online availability

10.1016/j.sysconle.2011.02.005

Library availability

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Cite this

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title = "On limitations in H∞ suboptimal decentralized control derived from the generalized structured singular value",

abstract = "We study how the maximum/minimum gain of a decentralized or sparse controller over a frequency interval influences the maximum/minimum gain of the corresponding closed-loop transfer function over that interval. In doing so, we derive lower bounds on the best closed-loop performance achievable by decentralized and sparse controllers satisfying additional frequency domain restrictions, and sufficient conditions for a structured controller to guarantee a desired level of closed-loop performance. This results in graphical tests for the controller's singular value plots. These bounds are obtained by using tools inspired by generalizations of the structured singular value, and can be computed by solving Linear Matrix Inequalities (LMI). We close by applying our results to an active sound control problem.",

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