Adela Ionescu†
Abstract: The problem of stabilization of dynamical systems is very important, as part of the control systems field. The theory of positive polynomials in control has the seeds in the 1980’s, based on the work of Naum Zuselevich. They can be used to solve a variety of problems in robust control, non-linear control and also in non-convex optimization. The present paper approaches the problem of finding a stabilizing feedback for homogeneous polynomial systems in the plane. It is known that the polynomial systems in the plane have a lot of special properties which can be easier approached thanks to the dimension 2. The case of systems arising from excitable media is taken into account, and the results will be used to deduce properties for further detailed analysis.
Keywords: kinematics of mixing, control, Lyapunov stability, polynomial system, feedback stabilization.
MSC: 93D15, 93D05, 34H15.
DOI 10.56082/annalsarscimath.2025.3.245
† adelajaneta2015@gmail.com, Department of Mathematics, University of Craiova, 13 A.I. Cuza Street, 200585 Craiova, Romania
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 3, 2025
