arXiv:1812.05360 Abstract | arXiv Analytics

arXiv:1812.05360 [math.NA]Abstract References Reviews Resources

Impulse response of bilinear systems based on Volterra series representation

Published 2018-12-13Version 1

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.

Comments: 34 pages, 8 figures

Categories: math.NA, cs.SY, math.DS

Subjects: 93C10, 93C15, 93A15

Keywords: volterra series representation, bilinear systems, nascent delta function, novel impulse response, well-known volterra kernels

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