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

• Published in: Automatica (Oxford) Vol. 50; no. 2; pp. 547 - 551
• Main Authors: Shen, Jun, Lam, James
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2014; Elsevier
• 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; Finite-time stability; Fractional-order nonlinear system; Equilibria; Linear Lyapunov function; Initial value problem; Non linear control; Delay system; Non linear system; Positive system; Modeling; Fractional derivative; Asymptotic stability; Time interval; Lyapunov function; Non existence

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...