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VOL. 37 | 1999 Balancing of diffusion partial differential equation


This paper concerns with the balancing theory for the system governed by diffusion partial differential equation, which is refereed here as infinite dimensional system or distributed-parameter system. Based on the eigenvalue-eigenfunction structure of Laplacian differential operator, the approximate controllability and initial observability are constructed. In order to perform the balanced realization for infinite dimensional system, a brief review on finite dimensional balancing is presented, and more intuitive meaning of balanced realization is then obtained. After defining the Hankel operator of the infinite dimensional system, we compute the Hankel singular value and construct the energy balancing. And then, the model reduction problem is discussed. In the sequel, numerical simulation of the balanced model reduction for one-dimensional heat equation is conducted.


Published: 1 January 1999
First available in Project Euclid: 18 November 2014

zbMATH: 1193.93110

Rights: Copyright © 1999, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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