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

Abstract

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.