.. title: A description of Port-Hamiltonian Systems
.. slug: a-description-of-port-hamiltonian-systems
.. date: 2015-10-10 13:22:44 UTC+02:00
.. tags: method, theoretical tools, mathjax
.. category: 
.. link: 
.. description: 
.. type: text

	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.

.. TEASER_END

.. math::

	\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}
	

.. slides::

   /galleries/demo/tesla_conducts_lg.jpg
   /galleries/demo/tesla_lightning2_lg.jpg
   /galleries/demo/tesla4_lg.jpg
   /galleries/demo/tesla_lightning1_lg.jpg
   /galleries/demo/tesla_tower1_lg.jpg

.. youtube:: 0WqAByOzQY0