Compositions of  passive boundary control systems

Atte Aalto; Jarmo Malinen

doi:10.3934/mcrf.2013.3.1

Article Contents

2013, Volume 3, Issue 1: 1-19. Doi: 10.3934/mcrf.2013.3.1

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Compositions of passive boundary control systems

Atte Aalto^1, and
Jarmo Malinen^1,

1.
Department of Mathematics and Systems Analysis, Aalto University School of Science, PB 11100, 00076-Aalto

Received: November 30, 2011

Revised: April 30, 2012

Published: February 2013

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Abstract

We show under mild assumptions that a composition of internally well-posed, impedance passive (or conservative) boundary control systems through Kirchhoff type connections is also an internally well-posed, impedance passive (resp., conservative) boundary control system. The proof is based on results of Malinen and Staffans [21]. We also present an example of such composition involving Webster's equation on a Y-shaped graph.

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Mathematics Subject Classification: Primary: 47A48; Secondary: 35R02, 47N70, 35L65.

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