Non-existence of finite-time stable equilibria in fractional-order nonlinear systems

We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that fo...

Full description

Saved in:
Bibliographic Details
Published in:Automatica (Oxford) 2014-02, Vol.50 (2), p.547-551
Main Authors: Shen, Jun, Lam, James
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Delay
Dynamical systems
Equilibria
Exact sciences and technology
Finite-time stability
Fractional-order nonlinear system
Initial value problems
Linear Lyapunov function
Lyapunov functions
Nonlinear dynamics
Stability
System theory
Trajectories
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.11.018