Evaluation of fractional order of the discrete integrator. Part II

Abstract

This is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

The Floquet-Lyapunov transformation for fractional discrete-time linear systems with periodic parameters

“…The fractional linear systems have been considered in many papers and books and many well-known results for standard linear systems have been extended to fractional linear systems [6][7][8][9][10][11]. The Floquet-Lyapunov transformation has been analyzed in many books and papers [1][2][3][4].…”