Observer normal forms for a class of nonlinear systems by means of coupled auxiliary dynamics
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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… read more here.
Keywords: auxiliary dynamics; dynamical systems; observer normal; class nonlinear ... See more keywords
Convergence to Normal Forms of Integrable PDEs
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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… read more here.
Keywords: integrable pdes; convergence normal; normal form; forms integrable ... See more keywords
Normal forms for rank two linear irregular differential equations and moduli spaces
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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… read more here.
Keywords: linear irregular; irregular differential; rank two; forms rank ... See more keywords
Normal forms of C∞ vector fields based on the renormalization group
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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… read more here.
Keywords: normal forms; renormalization group; vector fields; normal form ... See more keywords
Local Integrability of Poincaré–Dulac Normal Forms
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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… read more here.
Keywords: local integrability; poincar dulac; dulac normal; normal forms ... See more keywords
SECOND-ORDER NORMAL FORMS FOR N-DIMENSIONAL SYSTEMS WITH A NILPOTENT POINT
Sign Up to like & getrecommendations! 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… read more here.
Keywords: second order; complementary spaces; forms dimensional; order normal ... See more keywords