Extended Kalman-Yakubovich-Popov lemma in a Hilbert space and Fenchel duality.

被引：0
|
作者：
Gusev, Sergei V. [1 ]
机构：
[1] St Petersburg State Univ, Fac Math & Mech, St Petersburg 198904, Russia
来源：
2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8 | 2005年
关键词：
D O I：
暂无
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 (KYP) lemma is extended with new conditions that are equivalent to solvability of the Lur'e equation or the corresponding linear operator inequality. The relation established between the KYP lemma and an extremum problem on the set of positive semi-definite solutions of the generalized Lyapunov inclusion. It is proved that the statements of the KYP lemma are necessary and sufficient conditions for value to be bounded in this problem. The approach is based on the special Fenchel duality theorem and presents the new proof of the KYP lemma as well. The linear-quadratic optimization problem for a behavioral system in a Hilbert space is considered to illustrate the application of the new statements that are added to the KYP lemma.
引用
收藏
页码：1565 / 1570
页数：6
相关论文
共 50 条
  • [1] On the Kalman-Yakubovich-Popov lemma
    Rantzer, A
    SYSTEMS & CONTROL LETTERS, 1996, 28 (01) : 7 - 10
  • [2] On Kalman-Yakubovich-Popov Lemma for stabilizable systems
    Collado, J
    Lozano, R
    Johansson, R
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2001, 46 (07) : 1089 - 1093
  • [3] The Kalman-Yakubovich-Popov Lemma in a behavioural framework
    van der Geest, R
    Trentelman, H
    SYSTEMS & CONTROL LETTERS, 1997, 32 (05) : 283 - 290
  • [4] On the Kalman-Yakubovich-Popov lemma and the multidimensional models
    Bachelier, Olivier
    Paszke, Wojciech
    Mehdi, Driss
    MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 2008, 19 (3-4) : 425 - 447
  • [5] On the Kalman-Yakubovich-Popov Lemma for Positive Systems
    Rantzer, Anders
    2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2012, : 7482 - 7484
  • [6] The Kalman-Yakubovich-Popov Lemma in a behavioural framework
    Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands
    不详
    Syst Control Lett, 5 (283-290):
  • [7] On the Kalman-Yakubovich-Popov Lemma for Positive Systems
    Rantzer, Anders
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2016, 61 (05) : 1346 - 1349
  • [8] An alternative Kalman-Yakubovich-Popov lemma and some extensions
    Graham, Matthew R.
    de Oliveira, Mauricio C.
    de Callafon, Raymond A.
    AUTOMATICA, 2009, 45 (06) : 1489 - 1496
  • [9] Extension of Kalman-Yakubovich-Popov lemma to descriptor systems
    Camlibel, M. K.
    Frasca, R.
    SYSTEMS & CONTROL LETTERS, 2009, 58 (12) : 795 - 803
  • [10] A Kalman-Yakubovich-Popov Lemma with affine dependence on the frequency
    Graham, M. R.
    de Oliveira, M. C.
    2008 AMERICAN CONTROL CONFERENCE, VOLS 1-12, 2008, : 1086 - 1091
12345