Abstract
Dirac structures are used as the underlying structure to mathematically formalize port-Hamiltonian systems. This note approaches the Dirac structures for infinite-dimensional systems using the theory of linear relations on Hilbert spaces. First, a kernel representation for a Dirac structure is proposed. The one-to-one correspondence between Dirac structures and unitary operators is revisited. Further, the proposed kernel representation and a scattering representation are constructively related. Several illustrative examples are also presented in the paper.
| Original language | English |
|---|---|
| Pages (from-to) | 295-308 |
| Number of pages | 14 |
| Journal | Mathematical Modelling of Natural Phenomena |
| Volume | 9 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2014 |
Keywords
- Dirac structure
- linear relation
- Hilbert space
- infinite-dimensional system
- PORT-HAMILTONIAN SYSTEMS
- SPACES
- FLOW