## Title data

Benner, Peter ; Damm, Tobias:

**Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems.**

*In:* SIAM Journal on Control and Optimization.
Vol. 49
(2011)
Issue 2
.
- pp. 686-711.

ISSN 1095-7138

DOI: https://doi.org/10.1137/09075041X

## Abstract in another language

We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of stochastic and bilinear systems together with the corresponding energy functionals. While Gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems, the relation of Gramians and energy functionals for bilinear systems is less obvious. We discuss results from the literature for the latter problem and provide new characterizations of input and output energies of bilinear systems in terms of algebraic Gramians satisfying generalized Lyapunov equations. In any of the considered cases, the definition of algebraic Gramians allows us to compute balancing transformations and implies model reduction methods analogous to balanced truncation for linear deterministic systems. We illustrate the performance of these model reduction methods by showing numerical experiments for different bilinear systems.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Additional notes: | Zentralblattnummer: pre05931218 |

Keywords: | Lyapunov equations; Gramians; energy functionals; balanced truncation; model order reduction; bilinear systems; stochastic systems |

Subject classification: | Mathematics Subject Classification Code: 93A15 (93A30 93C10 93E20 93B40) |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | No |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 03 Mar 2021 13:35 |

Last Modified: | 23 Mar 2021 09:12 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63653 |