Kharitonovの定理の幾何学的解釈

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タイトル別名
  • A Geometrical Interpretation of Kharitonov's Theorem
  • Kharitonov ノ テイリ ノ キカガクテキ カイシャク

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説明

Kharitonov's theorem appeared originally in the late seventies in a Russian literature but at the beginning so much attention was not paid to it at least in the western countries. Recently the potentiality of this far striking result in the analysis and synthesis of robust systems or systems with uncertainty has been gradually recognized and several research works using this theorem have begun to be reported. However, it seems that the original proof of the theorem might give no clear insight into why one could obtain such a marvelously simple result, especially to people who are in the engineering side.<br>Motivated by this point, the present paper makes an attempt to provide an interpretation of the theorem from a little different viewpoint. Discussions form an alternative way of proving the theorem. Moreover, these results are explained as well in terms of Mikhailov's stability criterion, a familiar tool to engineers for analyzing and designing control systems. This geometric interpretation makes it possible to grasp the central idea behind the theorem intuitively. The whole discussions of the present paper are expected to give some suggestions for developing further “Kharitonov-like” theorems for equations of other types of systems such as discrete systems, time-delay systems and so forth.

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