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Published in 2020 at "International Journal of Robust and Nonlinear Control"
DOI: 10.1002/rnc.5027
Abstract: This work aims at developing a class of nonlinear dynamical systems that can be converted into nonlinear observer normal forms, which support the well‐known high gain observer. This will be performed by means of the…
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Keywords:
auxiliary dynamics;
dynamical systems;
observer normal;
class nonlinear ... See more keywords
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Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03661-8
Abstract: In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can…
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Keywords:
integrable pdes;
convergence normal;
normal form;
forms integrable ... See more keywords
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Published in 2021 at "Periodica Mathematica Hungarica"
DOI: 10.1007/s10998-021-00408-8
Abstract: We provide a unique normal form for rank two irregular connections on the Riemann sphere. In fact, we provide a birational model where we introduce apparent singular points and where the bundle has a fixed…
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Keywords:
linear irregular;
irregular differential;
rank two;
forms rank ... See more keywords
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Published in 2021 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0031043
Abstract: The normal form theory for polynomial vector fields is extended to those for C∞ vector fields vanishing at the origin. Explicit formulas for the C∞ normal form and the near identity transformation that brings a…
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Keywords:
normal forms;
renormalization group;
vector fields;
normal form ... See more keywords
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Published in 2018 at "Regular and Chaotic Dynamics"
DOI: 10.1134/s1560354718070080
Abstract: We consider dynamical systems in Poincaré–Dulac normal form having an equilibrium at the origin, and give a sufficient condition for them to be integrable, and prove that it is necessary for their special integrability under…
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Keywords:
local integrability;
poincar dulac;
dulac normal;
normal forms ... See more keywords
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Published in 2020 at "Journal of Applied Analysis and Computation"
DOI: 10.11948/20190393
Abstract: Normal forms theory is one of the most powerful tools for the study of nonlinear differential equations, in particular, for stability and bifurcation analysis. Many works paid attention to normal forms associated with nilpotent Jacobian…
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Keywords:
second order;
complementary spaces;
forms dimensional;
order normal ... See more keywords