## Title data

Grüne, Lars ; Philipp, Friedrich ; Schaller, Manuel:

**Strict dissipativity for generalized linear-quadratic problems in infinite dimensions.**

Bayreuth ; Ilmenau
,
2022
. - 12 p.

DOI: https://doi.org/10.48550/arXiv.2202.08178

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## Project information

Project financing: |
Deutsche Forschungsgemeinschaft DFG Grant 289034702 DFG Grant 430154635 DFG Grant 244602989 |
---|

## Abstract in another language

We analyze strict dissipativity of generalized linear quadratic optimal control problems on Hilbert spaces. Here, the term "generalized" refers to cost functions containing both quadratic and linear terms. We characterize strict pre-dissipativity with a quadratic storage function via coercivity of a particular Lyapunov-like quadratic form. Further, we show that under an additional algebraic assumption, strict pre-dissipativity can be strengthened to strict dissipativity. Last, we relate the obtained characterizations of dissipativity with exponential detectability.