Abstract
We study the behavior of a Hilbert network (i.e., a finite or countably infinite network whose variables are in a Hilbert space and in which the associated total energy is finite) whose elements are affected by perturbations. More specifically, we will give estimates for a change of the current distribution caused by (a) perturbations of the elements of the nominal network when the voltage sources are fixed, and (b) a change of voltage sources in a network whose elements are perturbed. The conditions given in our theorems imply insensitivity and robust stability of the nominal network. The applications of the results are illustrated by an example of an infinite network.
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References
V. Dolezal,Monotone Operators and Applications in Control and Network Theory, Elsevier, Amsterdam, 1979.
V. Dolezal, Some estimates pertaining to sensitivity and robust stability of input-output systems,Circuits, Systems and Signal Processing, Vol. 13, No. 5, 1994, pp. 545–570.
A. H. Zemanian,Infinite Electrical Networks, Cambridge Univ. Press, London and New York, 1991.
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This research was supported by the NSF Grant #DMS-9102910.
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Dolezal, V. Behavior of Hilbert networks under perturbations of their elements. Circuits Systems and Signal Process 14, 135–143 (1995). https://doi.org/10.1007/BF01183831
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DOI: https://doi.org/10.1007/BF01183831