Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

¹ Inria (CORIDA, CONGE) & ESA 7035 du CNRS (MMAS), bâtiment A, Université de Metz, 57045 Metz Cedex 01, France; xu@loria.fr.
² Inria (CORIDA, CONGE) & ESA 7035 du CNRS (MMAS), bâtiment A, Université de Metz, 57045 Metz Cedex 01, France; sallet@loria.fr.

Received: 6 August 2001
Revised: 23 January 2002

Abstract

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is regular and derive various properties of its transfer functions, which are potentially useful for controller design. Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems.