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The formal LaplaceBorel transform of Fliess operators and the composition product
 Inter. J. Math. Math. Sci., Article ID
, 2006
"... Abstract — In this paper, the formal LaplaceBorel transform of an analytic nonlinear inputoutput system is defined, specifically, an inputoutput system that can be represented as a Fliess operator. Using this concept and the composition product, an explicit relationship is then derived between th ..."
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Cited by 10 (8 self)
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Abstract — In this paper, the formal LaplaceBorel transform of an analytic nonlinear inputoutput system is defined, specifically, an inputoutput system that can be represented as a Fliess operator. Using this concept and the composition product, an explicit relationship is then derived between the formal LaplaceBorel transforms of the input and output signals. This provides an alternative interpretation of the symbolic calculus introduced by Fliess to compute the output response of such systems. Finally, it is shown that the formal LaplaceBorel transform provides an isomorphism between the semigroup of all well defined Fliess operators under composition and the semigroup of all locally convergent formal power series under the composition product. I.
GENERATING SERIES FOR INTERCONNECTED ANALYTIC NONLINEAR SYSTEMS
, 2005
"... Given two analytic nonlinear inputoutput systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection, and feedback connection. In each case, the corresponding generating series is produced ..."
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Cited by 10 (8 self)
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Given two analytic nonlinear inputoutput systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection, and feedback connection. In each case, the corresponding generating series is produced and conditions for the convergence of the corresponding Fliess operator are given. In the process, an existing notion of a composition product for formal power series has its set of known properties significantly expanded. In addition, the notion of a feedback product for formal power series is shown to be well defined in a broad context, and its basic properties are characterized.
The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems
, 1993
"... LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequencydomain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. ..."
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LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequencydomain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files.