The Lur'e equation in a behavioral context
Please always quote using this URN:urn:nbn:de:0296-matheon-9035
- The well-known Kalman-Yakubovich-Popov Lemma establishes an equivalence between dissipativity and the solvability of a linear matrix inequality. In this paper we strengthen this result by showing the equivalence of dissipativity to the solvability of a so-called Lur'e equation, which mainly is a linear matrix inequality with a rank minimizing condition. Finally, we apply the result to standard systems to obtain the well-known result about the solvability of the algebraic Riccati equation.
Author: | Tobias Brüll |
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URN: | urn:nbn:de:0296-matheon-9035 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/09/29 |
Release Date: | 2011/09/29 |
Tag: | Lur'e equation; Thompson canonical form; algebraic Riccati equation; dissipativity; para-Hermitian |
Institute: | Technische Universität Berlin |
Project: | D Optics and Electronics (Electronic and photonic devices) |
MSC-Classification: | 93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Axx General / 93A99 None of the above, but in this section |
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Axx General | |
Preprint Number: | 819 |