Article ID Journal Published Year Pages File Type
563673 Signal Processing 2011 10 Pages PDF
Abstract

Mastery of the initial conditions of fractional order systems remains an open problem, in spite of a great number of contributions. This paper proposes a solution dedicated to linear fractional differential equations (FDEs), which is based on an equivalence principle between the original system and an exactly equivalent infinite dimensional ordinary differential equation (ODE). This equivalence principle is derived from the fractional integration operator concept and the frequency distributed state space model of this operator. Thanks to this principle, the FDE initial conditions problem is converted into a conventional ODE initialization problem, however with an infinite dimensional state vector. Practical FDE initialization is performed using an observer based technique applied to the equivalent ODE; a numerical example demonstrates the efficiency of this approach.

Related Topics
Physical Sciences and Engineering Computer Science Signal Processing
Authors
, ,