Abstract
Examples are given concerning the range of applicability of recent representation results that provide a means of studying the input-output properties of nonlinear systems in terms of the familiar impulse-response concept, and which extend the concept of integral transformation to nonlinear maps. We show that such representations, which we call “g-” and “h-representations,” exist for important classes of systems governed by nonlinear integral equations. In particular, it is proved that a large class of maps that have Volterra series representations also have these representations.
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Ball, D., Sandberg, I.W. Systems which possessg- andh- Representations. Circuits Systems and Signal Process 8, 145–162 (1989). https://doi.org/10.1007/BF01599935
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DOI: https://doi.org/10.1007/BF01599935