This work deals with the positive stabilization of positive LTI (linear time-invariant) systems. First, we provide necessary and sufficient conditions for the stabilizability of such systems, via the study of polytopes and the corresponding sets of vertices. This part ends with the design of an algorithm synthesizing the main results developped so far, and allowing th check the positive stabilizability of positive systems and to design - if possible - a gain matrix for the positive stabilization of the system. Secondly, we study a particular case of positive system and apply to it the theory developped in the first part. More precisely, it concerns two tubular reactor models - namely plug-flow and axial dispersion reactors - which are initially described by partial differential equations. First, we discretize the system to obtain a finite-dimensional model, and then we analyze this model via the approach developped in the first section.
Stabilisation positive de systèmes différentiels linéaires: théorie et application aux réacteurs tubulaires
DEHAYE, J. (Author). 18 Jan 2011
Student thesis: Master types › Master in Mathematics