Normal forms of planar switching systems

Normal forms based fuzzy systems

Normal forms have been introduced as approximating relations for fuzzy relations. Moreover, they can be viewed as a formalization of a collection of fuzzy IF-THEN rules. Therefore, investigation of approximating abilities of normal forms together with determination of an appropriate inference engine contributes to building of fuzzy systems.

Unique Normal Forms for Nilpotent Planar Vector Fields

On p-normal forms of nonlinear systems

Using the differential-geometric control theory, we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to, via a change of coordinates and restricted smooth state feedback, a generalized normal form called —normal form, which includes Brunovsky canonical form and feedback linearizable systems in a lower-triangular form as its sp...

Normal Forms of Nonlinear Control Systems

Numerous papers were published during the last decade on the normal forms of nonlinear control systems with applications in bifurcation and its control. The approach is motivated by Poincaré’s theory of normal forms for classical dynamical systems using homogeneous transformations. In this paper, we summarize a variety of control system normal forms published in the literature so that the norma...

Resonant normal forms as constrained linear systems

We show that a nonlinear dynamical system in Poincaré-Dulac normal form (in R) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the system and identify a naturally invariant manifold for the flow of the “parent” linear system. The parent system is finite dimensional if the spectrum satisfies only ...