Generalized convergence analysis of the fractional order systems

Open Physics

Ruzitalab Ahmad¹  Farahi Mohammad Hadi²  Erjaee Gholamhossien³ 

[1] Department of Applied Mathematics, Ferdowsi University of Mashhad, International Campus, Mashhad, Iran;Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran;School of Physical Sciences, University of California, Irvine, United States of America;

关键词: contraction theory;    stability;    convergence;    fractional order systems;    02.30.xx;    02.30.yy;    05.45.xt;    47.27.ed;   

DOI  :  10.1515/phys-2018-0055

来源: DOAJ

【 摘 要 】

The aim of the present work is to generalize the contraction theory for the analysis of the convergence of fractional order systems for both continuous-time and discrete-time systems. Contraction theory is a methodology for assessing the stability of trajectories of a dynamical system with respect to one another. The result of this study is a generalization of the Lyapunov matrix equation and linear eigenvalue analysis. The proposed approach gives a necessary and sufficient condition for exponential and global convergence of nonlinear fractional order systems. The examples elucidate that the theory is very straightforward and exact.

【 授权许可】

Unknown