文章基本信息

标题：Application of Facial Reduction to H ∞ State Feedback Control Problem ∗
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作者：Hayato Waki ; Noboru Sebe
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2015
卷号：48
期号：14
页码：113-119
DOI：10.1016/j.ifacol.2015.09.443
语种：English
出版社：Elsevier
摘要：AbstractOne often encounters numerical difficulties in solving linear matrix inequality (LMI) problems obtained fromH∞control problems. We discuss the reason from the viewpoint of optimization. It is empirically known that a numerical difficulty occurs if the resulting LMI problem or its dual is not strongly feasible.In this paper, we provide necessary and sufficient conditions for LMI problem and its dual not to be strongly feasible, and interpret them in terms of control system. For this, facial reduction, which was proposed by Borwein and Wolkowicz, plays an important role. We show that a necessary and sufficient condition closely related to the existence of invariant zeros in the closed left-half plane in the system, and present a way to remove the numerical difficulty with the null vectors associated with invariant zeros in the closed left-half plane. Numerical results show that the numerical stability is improved by applying it.
关键词：KeywordsH∞controllinear matrix inequalitiesstate feedback controlfacial reductioninvariant zeros