Modified Euler-Frobenius Polynomials With Application to Sampled Data Modelling

The broad class of polynomials generally known as Eulerian or Euler-Frobenius polynomials has a rich history in Mathematics and Engineering. They have been generalised in several directions and find application in diverse areas ranging from sampled-data modelling and polynomial interpolation to wavelets. Here we describe a modified class of Euler-Frobenius polynomials which are functions of two independent variables. We show that the sampling zero (dynamics) of general linear and nonlinear systems can be described using this new class of polynomials when considering several non-standard sampled-data modelling problems, including when generalised hold functions are used to generate the input and when the continuous system has a time delay.