Fractional-order Systems and Controls pp 259-271 | Cite as

# Systems Identification

## Abstract

It has been experimentally observed or analytically found that both the time domain and frequency domain behaviors of some linear systems and processes do not fit the standard laws, *i.e.*, exponential evolution in time domain or integer-order slopes in their frequency responses. In the time domain, it has been shown that these complicated dynamics can be described by, (*i.e.*, the solutions of the constitutive equations are) generalized hyperbolic functions, \( \mathcal{F}^{k}_{\alpha , \beta} (z) \), defined as

In particular, the Mittag–Leffler function in two parameters is defined as

from which we can obtain the standard exponential, hyperbolic, or time-scaling functions as particular cases.

## Keywords

Fractional Calculus Constant Phase Element Transcendental Function Actuator Voltage Transfer Function Model## Preview

Unable to display preview. Download preview PDF.