A description of Port-Hamiltonian Systems
Here we details the pH approach to the passive modeling and simulation of complex, multiphysics systems.
- We recall some notions from system theory (state space, passivity, lyapunov function, etc.)
- We give the port-Hamiltonian structure as introuced by A.J. Van der Schaft and B. Maschke
- We show how to build this structure automatically from a netlits description.
\begin{equation*}
\begin{array}{rcl}
\dot{\mathbf{x}} &=& \left( \mathbf{J}-\mathbf{R} \right) \cdot \nabla\mathtt{H}(\mathbf{x}) + \mathbf{G}\cdot \mathbf{u} \\
\mathbf{y} &=& \mathbf{G}^\intercal \cdot \nabla\mathtt{H}(\mathbf{x}) + \mathbf{D}\cdot \mathbf{u}
\end{array}
\end{equation*}
