Impulse response of bilinear systems based on Volterra series representation

2018/12/13 by María Cruz de Carlos Varona, Varona, Maria Cruz, Raphael Gebhart +1
Decision Sciences · Engineering · Physics and Astronomy · #93A15 #93C10 #93C15 #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1812.05360

openalex publication_date 2018/12/13 · openalex created_date 2018/12/22 · openalex updated_date 2026/07/28

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.

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