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# Global Stabilization of a Class of Partially Known Positive Systems

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1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this report we deal with the problem of global output feedback stabilization of a class of $n$-dimensional nonlinear positive systems possessing a one-dimensional unknown, though measured, part. We first propose our main result, an output feedback control procedure, taking advantage of measurements of the uncertain part, able to globally stabilize the system towards an adjustable equilibrium point in the interior of the positive orthant. Though quite general, this result is based on hypotheses that might be difficult to check in practice. Then in a second step, through a Theorem on a class of positive systems linking the existence of a strongly positive equillibrium to its global asymptotic stability, we propose other hypotheses for our main result to hold. These new hypotheses are more restrictive but much simpler to check. Some illustrative examples, highlighting both the potential complex open loop dynamics (multi-stability, limit cycle, chaos) of the considered systems and the interest of the control procedure, conclude this report.
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https://hal.inria.fr/inria-00086788
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Submitted on : Friday, July 28, 2006 - 6:01:41 PM
Last modification on : Tuesday, May 10, 2022 - 3:00:38 PM
Long-term archiving on: : Monday, September 20, 2010 - 4:37:43 PM

### Citation

Jean-Luc Gouzé, Olivier Bernard, Ludovic Mailleret. Global Stabilization of a Class of Partially Known Positive Systems. [Research Report] RR-5952, INRIA. 2006, pp.24. ⟨inria-00086788v2⟩

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