Paper Info
Title
Generalized S-procedure for inequality conditions on one-vector-lossless sets and linear system analysis
Abstract
The generalized S-procedure, introduced by Iwasaki et al. (2000), has proved to be very useful for robustness analysis and synthesis of control systems. This procedure provides a nonconservative way to convert inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a notion, one-vector-lossless sets, and propose a generalized S-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized S-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities for stability analysis of linear systems and LMIs for state-feedback controller synthesis can be viewed as particular cases of this result.
Year
DOI
Venue
2008
10.1109/CDC.2004.1430217
Decision and Control, 2004. CDC. 43rd IEEE Conference
Keywords
DocType
Volume
Lyapunov methods,control system synthesis,linear matrix inequalities,linear systems,polynomial matrices,robust control,state feedback,Lyapunov inequalities,control system synthesis,full rank property analysis,generalized S-procedure,linear matrix inequalities,linear system analysis,matrix-valued functions,one-vector-lossless sets,polynomial matrices,robustness analysis,stability analysis,state-feedback controller synthesis
Journal
2
Issue
ISSN
ISBN
3
0191-2216
0-7803-8682-5
Citations 
PageRank 
References 
8
1.37
3
Authors
3
Name
Order
Citations
PageRank
Yoshio Ebihara116419.52
Katsutoshi Maeda281.37
Tomomichi Hagiwara328653.12