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In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator S := [ A&B C&D ] : D(S)→ [Y ] where X is the state space and Y is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated… (More)

- J. A. Villegas
- 2005

We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance energy-preserving system, as well as scattering energy-preserving system. For the first type of systems we consider (static and dynamic) feedback stabilization… (More)

In this paper we study a class of partial differential equations (PDE’s), which includes SturmLiouville systems and diffusion equations. From this class of PDE’s we define systems with control and observation through the boundary of the spatial domain. That is, we describe how to select boundary conditions, such that the resulting system has inputs and… (More)

- Y. Le Gorrec, Bernhard Maschke, J. A. Villegas, Hans Zwart
- 2006 IEEE Conference on Computer Aided Control…
- 2006

In this paper we consider distributed parameter physical systems composed of a reversible part associated with a skew-symmetric operator J as Hamiltonian systems (Olver, 1993) and a symmetric operator associated with some irreversible phenomena. We will show how to use results obtained on reversible systems to parametrize the boundary conditions such that… (More)

- J. A. Villegas
- 2005

This article studies the telegrapher’s equations with boundary port variables. Firstly, a link is made between the telegrapher’s equations and a skewsymmetric linear operator on a spatial domain. Associated to this linear operator is a Dirac structure which includes the port variables on the boundary of this spatial domain. Secondly, we present all… (More)

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