Positive control for global stabilization of predator-prey systems

Frédéric Grognard 1 Jonathan Rault 1, 2 Jean-Luc Gouzé 1
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
Abstract : In this paper we propose a positive linear control law for the stabilization of positive equilibria in predator-prey systems. This problem is motivated by the introduction, which is by essence positive, of predators in biological control applications, to prevent excessive levels of prey (pests). We build a linear controller that we saturate at zero and prove, under some conditions, the global asymptotic stability of the equilibrium. Without one of these conditions, the point is shown to be globally attractive but may be unstable.
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Communication dans un congrès
Tarbouriech, Sophie and Krstic, Miroslav. 9th IFAC Symposium Nonlinear Control Systems (NOLCOS'13), 2013, Toulouse, France. IFAC, 9 Part 1, pp.265-270, 2013, Nonlinear Control Systems. 〈10.3182/20130904-3-FR-2041.00136〉
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https://hal.inria.fr/hal-00850374
Contributeur : Jean-Luc Gouzé <>
Soumis le : mardi 6 août 2013 - 12:57:22
Dernière modification le : mercredi 21 mars 2018 - 18:57:45

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Frédéric Grognard, Jonathan Rault, Jean-Luc Gouzé. Positive control for global stabilization of predator-prey systems. Tarbouriech, Sophie and Krstic, Miroslav. 9th IFAC Symposium Nonlinear Control Systems (NOLCOS'13), 2013, Toulouse, France. IFAC, 9 Part 1, pp.265-270, 2013, Nonlinear Control Systems. 〈10.3182/20130904-3-FR-2041.00136〉. 〈hal-00850374〉

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