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

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 syst...

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Published inIEEE transactions on automatic control Vol. 61; no. 9; pp. 2676 - 2681
Main Authors Jun Shen, Lam, James
Format Journal Article
LanguageEnglish
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
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Abstract 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.
AbstractList This paper addresses the stability and $L_{\infty}$-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 $L_{\infty}$-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.
This paper addresses the stability and [Formula Omitted]-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 [Formula Omitted]-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.
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.
Author Jun Shen
Lam, James
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  fullname: Jun Shen
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  givenname: James
  surname: Lam
  fullname: Lam, James
  email: james.lam@hku.hk
  organization: Dept. of Mech. Eng., Univ. of Hong Kong, Hong Kong, China
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Snippet This paper addresses the stability and L ∞ -gain analysis problem for continuous-time positive fractional-order delay systems with incommensurate orders...
This paper addresses the stability and [Formula Omitted]-gain analysis problem for continuous-time positive fractional-order delay systems with incommensurate...
This paper addresses the stability and $L_{\infty}$-gain analysis problem for continuous-time positive fractional-order delay systems with incommensurate...
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SubjectTerms 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
Title Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays
URI https://ieeexplore.ieee.org/document/7342920
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