Measuring How Far a Controllable System is from an Uncontrollable One

Daniel L. Boley, Wu Sheng Lu

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The main goal of this note is to explore some of the properties of a controllable system which, in a precise sense to be defined, is near an uncontrollable pair. To do this, we first discuss the notion of the distance between a controllable system and the nearest uncontrollable one in both real and complex cases [2]–[5]. When this distance is relatively small, we show to what extent this distance corresponds to certain properties of the uncontrollability matrix and the reachability Grammian.

Original languageEnglish (US)
Pages (from-to)249-251
Number of pages3
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Mar 1986

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