Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 61, Issue 9, Pages 2676-2681Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2015.2504516
Keywords
Fractional-order systems; positive systems; time-delay systems
Funding
- GRF [HKU17204014]
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This paper addresses the stability and L-infinity-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-infinity-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.
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