Title :
Lyapunov stability of fractional order systems: The two derivatives case
Author :
Trigeassou, Jean-Claude ; Maamri, Nezha ; Oustaloup, Alain
Author_Institution :
LAPS, Univ. of Bordeaux, Bordeaux, France
Abstract :
Lyapunov stability of linear commensurate order fractional systems is investigated in this paper. The connection between the fractional system poles and the decrease of the fractional Lyapunov function is presented as the key point to analyze system stability. LMI conditions depending on the A matrix eigenvalues are derived for a two derivatives fractional differential equation, which is considered as a generic case for more complex systems.
Keywords :
Lyapunov methods; differential equations; eigenvalues and eigenfunctions; large-scale systems; linear matrix inequalities; linear systems; poles and zeros; stability; A matrix eigenvalues; LMI conditions; Lyapunov stability; complex systems; derivative fractional differential equation; fractional Lyapunov function reduction; fractional order systems; linear commensurate order fractional system poles; system stability analysis; Differential equations; Educational institutions; Eigenvalues and eigenfunctions; Equations; Lyapunov methods; Mathematical model; Stability analysis; LMI stability conditions; Lyapunov stability; fractional differential equations; fractional energy; infinite state approach;
Conference_Titel :
Fractional Differentiation and Its Applications (ICFDA), 2014 International Conference on
Conference_Location :
Catania
DOI :
10.1109/ICFDA.2014.6967451
