Complex-fractional systems: Modal decomposition and stability condition

Author

Cois, O. ; Levron, F. ; Oustaloup, A.

Author_Institution

Lab. d´Autom. et de Productique, Univ. Bordeaux I, Talence, France

fYear

2001

fDate

4-7 Sept. 2001

Firstpage

1484

Lastpage

1489

Abstract

Complex-fractional systems are systems that are governed by a differential equation characterized by complex order fractional derivatives. A new modeling tool is proposed and used to study these systems: complex order state-space representation. The tool results from the extension of the differentiation order, from order 1 to complex order, in the state equation of classical state-space representation: A modal decomposition of complex-fractional systems and an analytical expression of their output are given. A stability condition is then established. Finally, an academic example illustrates results.

Keywords

differential equations; differentiation; large-scale systems; stability; state-space methods; complex order fractional derivatives; complex order state-space representation; complex-fractional systems; differential equation; differentiation order; modal decomposition; stability condition; Differential equations; Eigenvalues and eigenfunctions; Equations; Europe; Laplace equations; Mathematical model; Stability analysis; complex order fractional derivative; complex order state-space representation; complex-fractional system; modal decomposition; stability condition;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ECC), 2001 European

Conference_Location

Porto

Print_ISBN

978-3-9524173-6-2

Type

conf

Filename

7076128