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Colloquium Mathematics, Professor Hans Zwart (UT)

15 January 2013

Join us for coffee and tea at 15.30 p.m.

Date:                           Tuesday, January 15th 2013

Speaker:                     Professor Hans Zwart,
Department of Applied Mathematics, University of Twente

Room:                         5161.0267 (Bernoulliborg)

Time:                           16.00

Title: Linear port Hamiltonian Systems


The field of infinite-dimensional systems theory has become a well-established field within mathematics and systems theory. There are basically two approaches to infinite-dimensional linear systems theory: an  abstract functional analytical approach and  a PDE approach.
Many physical systems can be formulated using a Hamiltonian framework. This class contains ordinary as well as partial differential equations. Each system in this class has a Hamiltonian, generally given by the energy function. In the study of Hamiltonian systems it is usually assumed that the system does not interact with its environment. However, for the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take this interaction with the environment into account. This led to the class of port-Hamiltonian systems. For port-Hamiltonian systems described by ordinary differential equations this approach is very successful. Port-Hamiltonian systems described by partial differential equation is a subject of current research.

In this presentation, we combine the abstract functional analytical approach with the more physical approach based on Hamiltonians. For a class of linear infinite-dimensional port-Hamiltonian systems we derive easy verifiable conditions for the existence of solutions. Furthermore, we show that these solutions relate in a natural manner the external and internal energy of the system.

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : and

Dr. A.V. Kiselev (e-mail:

Last modified:06 June 2018 2.04 p.m.

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