Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays

• Published in: IEEE transactions on automatic control Vol. 61; no. 9; pp. 2676 - 2681
• Main Authors: Jun Shen, Lam, James
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Asymptotic stability; Automatic control; Constants; Delay; Delay systems; Delays; Fractional-order systems; Lyapunov methods; Mathematical models; positive systems; Stability; Stability criteria; time-delay systems; Time-varying systems; Trajectories
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2504516

This paper addresses the stability and L ∞ -gain analysis problem for continuous-time positive fractional-order delay systems with incommensurate orders between zero and one. A necessary and sufficient condition is firstly given to characterize the positivity of continuous-time fractional-order systems with bounded time-varying delays. Moreover, by exploiting the monotonic and asymptotic property of the constant delay system by virtue of the positivity, and comparing the trajectory of the time-varying delay system with that of the constant delay system, it is proved that the asymptotic stability of positive fractional-order systems is not sensitive to the magnitude of delays. In addition, it is shown that the L ∞ -gain of a positive fractional-order system is independent of the magnitude of delays and fully determined by the system matrices. Finally, a numerical example is given to show the validity of the theoretical results.