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

被引：11
|
作者：
Reis, Timo [1 ]
Voigt, Matthias [2 ]
机构：
[1] Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany
[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany
来源：
SYSTEMS & CONTROL LETTERS | 2015年 / 86卷
关键词：
Differential-algebraic equation; Kalman-Yakubovich-Popov lemma; Popov function; Bounded real lemma; Positive real lemma; RICCATI EQUATION; AUTOMATIC CONTROL;
D O I：
10.1016/j.sysconle.2015.09.003
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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. (C) 2015 Elsevier B.V. All rights reserved.
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页码：1 / 8
页数：8
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