Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Robust H Performance Analysis of LTI Systems with a Single Uncertain Parameter
—Asymptotically Exact Construction of a Sequence of Relaxation Problems via Dual LMIs and Non-Asymptotic Exactness Verification
Yusuke MatsudaMasato TaharaYoshio EbiharaTomomichi Hagiwara
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2010 Volume 23 Issue 3 Pages 46-55


This paper addresses the robust H performance analysis problem of linear time-invariant (LTI) systems whose state-space coefficient matrices depend polynomially on a single uncertain parameter. By means of a dual LMI that characterizes the H performance of uncertainty-free LTI systems, we firstly formulate this analysis problem as a polynomial matrix inequality (PMI) optimization problem. However, this PMI problem is non-convex and hence intractable in general. Therefore, we apply linearization and construct an infinite sequence of relaxation problems, represented by SDPs, with theoretical guarantee of asymptotic exactness in the limit. In order to detect whether an arbitrary relaxation problem in the sequence is “exact” in the sense that it provides the same optimal value as that of the original problem, we derive a rank condition on the SDP solution under which we can conclude the exactness.

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© 2010 The Institute of Systems, Control and Information Engineers
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