Robust H.INF. 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

Autor:	Tomomichi Hagiwara, Masato Tahara, Yusuke Matsuda, Yoshio Ebihara
Rok vydání:	2010
Předmět:	Mathematical optimization Sequence Optimization problem Computer Science::Systems and Control Linearization Rank condition Limit (mathematics) Relaxation (approximation) Polynomial matrix Dual (category theory) Mathematics
Zdroj:	Transactions of the Institute of Systems, Control and Information Engineers. 23:46-55
ISSN:	2185-811X 1342-5668
DOI:	10.5687/iscie.23.46
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b7dfb4b0fc6c431c8a4e5127ee92e78a https://doi.org/10.5687/iscie.23.46 Zobrazit plný text záznamu