A riesz basis methodology for proportional and integral output regulation of a one-dimensional diffusive-wave equation

Boumediène Chentouf, Jun Min Wang

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12 Citations (Scopus)


In this article, we consider a dam-river system modeled by a diffusive-wave equation. This model is commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important. In order to stabilize and regulate the system, we propose a proportional and integral boundary controller. Contrary to many physical systems, we end up with a nondissipative closed-loop system with noncollocated actuators and sensors. We show that the closed-loop system is a Riesz spectral system and generates an analytic semigroup. Then, we shall be able to assign the spectrum of the closed-loop system in the open left half-plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation. These results are illustrated by several numerical examples.

Original languageEnglish
Pages (from-to)2275-2302
Number of pages28
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 2008



  • Analytic semigroup
  • Dam-river system
  • Proportional and integral boundary control
  • Riesz basis
  • Stability

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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