APPLICATION OF POLYNOMIAL SYSTEMS THEORY TO NONLINEAR SYSTEMS

2005 ◽  
Vol 38 (1) ◽  
pp. 987-992 ◽  
Author(s):  
Raimo Ylinen
Keyword(s):  
Nonlinear Systems ◽  
Systems Theory ◽  
Polynomial Systems

scholarly journals Saleh’s Model of AM/AM and AM/PM Conversions is not a Model without Memory – Another Proof

2017 ◽  
Vol 63 (1) ◽  
pp. 73-77
Author(s):  
Andrzej Borys
Keyword(s):  
Nonlinear Systems ◽  
Systems Theory ◽  
Power Amplifiers ◽  
Nonlinear Operator ◽  
Common View ◽  
Baseband Signal ◽  
Equivalent Description

Abstract The so-called Saleh’s representation for description of the AM/AM and AM/PM conversions, occurring in communication power amplifiers, consists of two expressions that describe them as functions of a real-valued baseband signal modulating the carrier amplitude. It is a common view that this description forms a model without memory. We show here that the above belief is not correct; just the opposite is true. To prove this, we take into account an equivalent description of the Saleh’s model called the quadrature model of bandpass nonlinearities and express it in a form of a nonlinear operator. Afterwards, we check whether this operator possesses a zero memory. To this end, we use an appropriate theorem of the nonlinear systems theory. Finally, as a result of this investigation, we observe that the memory of the above operator is nonzero.

scholarly journals DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART II: THREE-MANIFOLDS, HEEGAARD SPLITTINGS AND THREE-DIMENSIONAL SYSTEMS

2007 ◽  
Vol 17 (06) ◽  
pp. 2085-2095 ◽  
Author(s):  
YI SONG ◽  
STEPHEN P. BANKS
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Systems Theory ◽  
Topological Structure ◽  
Three Dimensional ◽  
Local System ◽  
Operating Point ◽  
Global Behavior ◽  
Heegaard Splittings

The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with "arbitrarily strange" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.

Nonlinear Systems Theory (John L. Casti)

SIAM Review ◽  
1988 ◽  
Vol 30 (1) ◽  
pp. 156-165
Author(s):  
H. J. Sussmann
Keyword(s):  
Nonlinear Systems ◽  
Systems Theory

On global and local observability of nonlinear polynomial systems: a decidable criterion

2020 ◽  
Vol 68 (6) ◽  
pp. 395-409 ◽  
Author(s):  
Daniel Gerbet ◽  
Klaus Röbenack
Keyword(s):  
Algebraic Geometry ◽  
Nonlinear Systems ◽  
Polynomial Systems ◽  
Sufficient Condition ◽  
Rank Condition ◽  
Observability Analysis ◽  
Global And Local

AbstractIt is very difficult to check the observability of nonlinear systems. Even for local observability, the observability rank condition provides only a sufficient condition. Much more difficult is the verification of global observability. This paper deals with the local and global observability analysis of polynomial systems based on algebraic geometry. In particular, we derive a decidable criterion for the verification of global observability of polynomial systems. Our framework can also be employed for local observability analysis.

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