Paper Info
Title
Robust Performance Analysis of Uncertain LTI Systems: Dual LMI Approach and Verifications for Exactness
Abstract
This paper addresses robust performance analysis problems of linear time-invariant (LTI) systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution. By pursuing this direction, in this paper, we provide rank conditions on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can be computed. These results come from block-moment matrix structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions for the exactness verification can be obtained.
Year
DOI
Venue
2009
10.1109/TAC.2009.2017086
IEEE Trans. Automat. Contr.
Keywords
DocType
Volume
Robustness,Performance analysis,Linear matrix inequalities,Uncertainty,NP-hard problem,Linear systems,Polynomials,Control theory,Educational technology,Transfer functions
Journal
54
Issue
ISSN
ISBN
5
0018-9286
978-1-4244-1498-7
Citations 
PageRank 
References 
8
0.83
22
Authors
3
Name
Order
Citations
PageRank
Yoshio Ebihara116419.52
Yusuke Onishi280.83
Tomomichi Hagiwara328653.12