Positive Stabilization of a Class of Infinite-Dimensional Positive Systems

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 471)


For a class of positive unstable infinite-dimensional linear systems, a method is described for computing a positively stabilizing state feedback, such that the resulting input trajectory remains in an affine cone. This design results in a possibly negative lower bound on the input, which makes the resulting closed-loop system stable and which maintains the nonnegativity of the state trajectory for specific initial states.


Infinite dimensional systems Positive linear systems Positive stabilization State feedback Affine cone 



The authors wish to thank the following persons with whom they have worked jointly on dynamical analysis and control of positive systems for many years: B. Abouzaid (Ecole Nationale des Sciences Appliquées, Université Chouaib Doukkali, El Jadida., Morocco), Ch. Beauthier (Cenaero, Gosselies, Belgium), D. Dochain (Université Catholique de Louvain, Belgium), M. Laabissi (Université Chouaib Doukkali, El Jadida, Morocco) and V. Wertz (Université Catholique de Louvain, Belgium).

This chapter presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculté des Sciences El Jadida, Département de MathématiquesUniversité Chouaib DoukkaliEl JadidaMorocco
  2. 2.Department of Mathematics and naXysUniversity of NamurNamurBelgium

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