Positive stabilization of a diffusion system by nonnegative boundary control

Jonathan N. Dehaye, Joseph J. Winkin

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution


This chapter deals with the issue of considering nonnegative inputs in the positive stabilization problem. It is shown in two different ways why one cannot expect to positively stabilize a positive system by use of a nonnegative input, first by a classical approach with a formal proof, then by working on an extended system for which the new input corresponds to the time derivative of the nominal one, thus circumventing the sign restriction. However, it is shown via a classical example of positive system—the pure diffusion system—that positively stabilizing a positive system with a nonnegative input is in some way possible: using a boundary control, the input sign depends on whether the boundary control appears in the boundary conditions or in the dynamics. The chapter then provides a parameterization of all positively stabilizing feedbacks for a discretized model of the pure diffusion system, some numerical simulations and a convergence discussion which allows to extend the results to the infinite-dimensional case, where the system is described again by a parabolic partial differential equation and the input acts either in the dynamics or in the boundary conditions.

Original languageEnglish
Title of host publicationPositive Systems
Subtitle of host publicationTheory and Applications (POSTA 2016) Rome, Italy, September 14-16, 2016
EditorsFilippo Cacace, Lorenzo Farina, Roberto Setola, Alfredo Germani
PublisherSpringer Verlag
Number of pages12
ISBN (Electronic)978-3-319-54211-9
ISBN (Print)9783319542102
Publication statusPublished - 1 Jan 2017
Event5th International Symposium on Positive Systems, POSTA 2016 - Rome, Italy
Duration: 14 Sep 201616 Sep 2016

Publication series

NameLecture Notes in Control and Information Sciences
ISSN (Print)0170-8643
ISSN (Electronic)1610-7411


Conference5th International Symposium on Positive Systems, POSTA 2016
City Rome


  • Diffusion equation
  • Feedback parameterization
  • Nonnegative input
  • Partial differential equations
  • Positive stabilization
  • Positive systems

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