Invariant stabilization of discretized boundary control systems

Student thesis: Doc typesDoctor of Sciences

Abstract

Stabilization and invariance are the two keywords of this work. By invariant stabilization, one should understand the asymptotic stabilization of a system while keeping the state trajectories in a predetermined domain. First, we deal with the positive linear time-invariant (LTI) finite-dimensional systems for which we discuss the relevance of choosing a nonnegative input for the stabilization process, we provide a parameterization of all positively stabilizing feedbacks for a particular class of positive systems, and we extend the concept of invariance to cones, sectors and Lyapunov level sets. Then, we adapt the results to the positive LTI infinite-dimensional systems, we explain how one can switch from an input acting in the boundary conditions to an input acting in the dynamics, we introduce the standard example of the pure diffusion,
and we discuss the boundary conditions when discretizing a PDE system. Finally, we deal with the positive nonlinear time-invariant (NTI) infinite-dimensional systems, for which we once again adapt the previous theoretical results and consider a relevant example, namely a biochemical reactor model.
Date of Award25 Oct 2017
Original languageEnglish
Awarding Institution
  • University of Namur
SponsorsPAI City and society
SupervisorJoseph Winkin (Supervisor), Anne Lemaitre (President), Alexandre Mauroy (Jury), Alain Vande Wouwer (Jury) & Christophe Prieur (Jury)

Attachment to an Research Institute in UNAMUR

  • naXys

Cite this

Invariant stabilization of discretized boundary control systems
Dehaye, J. (Author). 25 Oct 2017

Student thesis: Doc typesDoctor of Sciences