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Title: Robust decentralized $H_2$ control of multi-channel descriptor systems with norm-bounded parametric uncertainties (English)
Author: Gui, Weihua
Author: Chen, Ning
Author: Zhai, Guisheng
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 45
Issue: 1
Year: 2009
Pages: 49-62
Summary lang: English
Category: math
Summary: This paper considers a robust decentralized $H_2$ control problem for multi-channel descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified $H_2$ norm is derived in terms of a strict nonlinear matrix inequality (NMI), that is, an NMI with no equality constraint. A two-stage homotopy method is proposed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the efficiency of this method. (English)
Keyword: decentralized control
Keyword: descriptor systems
Keyword: parametric uncertainty
Keyword: homotopy method
Keyword: nonlinear matrix inequality
MSC: 93A14
MSC: 93B40
MSC: 93B51
MSC: 93B52
MSC: 93C15
idZBL: Zbl 1158.93304
idMR: MR2489580
Date available: 2010-06-02T18:18:44Z
Last updated: 2012-06-06
Stable URL:
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