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.
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| Author: | Tobias Brüll |
|---|---|
| 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 |
