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Impulse response of bilinear systems based on Volterra series representation (1812.05360v2)
Published 13 Dec 2018 in math.NA, cs.SY, and math.DS
Abstract: This paper focuses on the systems theory of bilinear dynamical systems using the Volterra series representation. The main contributions are threefold. First, we gain an input-output representation in the frequency domain, where the Laplace transform of the kernels can indeed be interpreted as transfer functions. Then, we derive the response of bilinear systems to a nascent delta function in time domain, i.e. the impulse response of bilinear systems. Finally, we study the relationships between this novel impulse response and the well-known Volterra kernels and adjust those to be compatible to the impulse response.