Reprint of “The Kalman-Yakubovich-Popov inequality for differential-algebraic systems: Existence of nonpositive solutions”

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• 作者：Timo Reis^a ; ^{timo.reis@math.uni-hamburg.de" class="auth_mail" title="E-mail the corresponding author} ; Matthias Voigt^b ; ^{mvoigt@math.tu-berlin.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Differential-algebraic equation ; Kalman&ndash ; Yakubovich&ndash ; Popov lemma ; Popov function ; Bounded real lemma ; Positive real lemma
• 刊名：Systems & Control Letters
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：95
• 期：Complete
• 页码：3-10
• 全文大小：444 K

文摘

The Kalman–Yakubovich–Popov lemma is a central result in systems and control theory which relates the positive semidefiniteness of a Popov function on the imaginary axis to the solvability of a linear matrix inequality. In this paper we prove sufficient conditions for the existence of a nonpositive solution of this inequality for differential-algebraic systems. Our conditions are given in terms of positivity of a modified Popov function in the right complex half-plane. Our results also apply to non-controllable systems. Consequences of our results are bounded real and positive real lemmas for differential-algebraic systems.