Proving the Convergence to Limit Cycles using Periodically Decreasing Jacobian Matrix Measures

Authors :: Jerray, Jawher
Saoud, Adnane
Fribourg, Laurent
Laboratoire Traitement et Communication de l'Information (LTCI)
Institut Mines-Télécom [Paris] (IMT)-Télécom Paris
Laboratoire Méthodes Formelles (LMF)
Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)
Laboratoire d'Informatique de Paris-Nord (LIPN)
Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Laboratoire des signaux et systèmes (L2S)
CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
Source :: European Journal of Control, European Journal of Control, 2022
Publication Year :: 2023
Publisher :: HAL CCSD, 2023.
Abstract: Methods based on "(Jacobian) matrix measure" to show the convergence of a dynamical system to a limit cycle (LC), generally assume that the measure is negative everywhere on the LC. We relax this assumption by assuming that the matrix measure is negative "on average" over one period of LC. Using an approximate Euler trajectory, we thus present a method that guarantees the LC existence, and allows us to construct a basin of attraction. This is illustrated on the example of the Van der Pol system.<br />Comment: 6 pages, 3 figures

Subjects :: Euler approximation
FOS: Electrical engineering, electronic engineering, information engineering
[INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY]
[INFO]Computer Science [cs]
Systems and Control (eess.SY)
Dynamical system
Limit cycle
dynamical systems
Jacobian Matrix
Electrical Engineering and Systems Science - Systems and Control

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