Abstract
A representation theorem for ground stable nonlinear systems with piecewise-constant inputs is presented. It is a three-dimensional system of differential equations augmented by an algebraic output equation. The representation is characterized by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N + 6</tex> parameters, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the number of harmonics used to represent transients. Five of the parameters are positive constants, and the remaining <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N + 1</tex> parameters are functions of either <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</tex> variables. Applications involving the macromodeling of higher dimensional linear and nonlinear systems are presented.
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