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M. Renardy and R. C. Rogers,” An Introduction to Partial Dif ferential Equations,” Springer, New York, 1993.

has been cited by the following article:

• TITLE: Observer for Linear Distributed-Parameter Systems with Application to Isothermal Plug-Flow Reactor

  AUTHORS: Nadia Barje, Mohamed Elarbi Achhab, Vincent Wertz

  KEYWORDS: Distributed-Parameter Systems; C0-semigroup; Exponential Observers; Perturbed Systems; Tubular Reactor

  JOURNAL NAME: Intelligent Control and Automation, Vol.4 No.4, November 13, 2013

  ABSTRACT: This paper presents a conception of an exponential observer for a class of linear distributed-parameter systems (DPSs), in which the dynamics are partially unknown. The given distributed-parameter observer ensures asymptotic state estimator with exponentially decay error, based on the theory of C0-semigroups in a Hilbert space. The theoretical observer developed is applied to a chemical tubular reactor, namely the isothermal Plug-Flow reactor basic dynamical model for which measurements are available at the reactor output only. The process is described by Partial differential equations with unknown initial states. For this application, performance issues are illustrated in a simulation study.