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Exponential describing function in the analysis of nonlinear systems

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1 Author(s)
Bickart, Theodore A. ; Syracuse University, Syracuse, NY, USA

In this paper, signals in(L)_{2}(- infty, t], a subspace of the space of square integrable signals defined on(- infty, t], are approximated by signals in(L)_{2}^{1}(- infty, t], the one-dimensional subspace of(L)_{2}(- infty, t]spanned by the first function from the set of reversed time Laguerre functions. A system mapping(L)_{2}(- infty, t]into itself is associated with a system mapping(L)_{2}^{1}(- infty t]into itself; the latter system is characterized by a gain-exponential describing function. This type of describing function is developed as an analysis tool for studying the transient response of a large class of nonlinear feedback systems. The contraction-mapping fixed-point theorem is used to develop conditions for the existence of a solution prior to the use of the exponential describing function to obtain an approximate solution.

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Automatic Control, IEEE Transactions on  (Volume:11 ,  Issue: 3 )