Positive Fractional-order Systems Research Articles

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

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.

State-dependent switching control of switched positive fractional-order systems

In this paper, the problem of switching stabilization for a class of continuous-time switched positive fractional-order systems is studied by using state-dependent switching. First, the asymptotic stability condition of switched positive fractional-order systems with state-dependent switching is given, which is based on the fractional co-positive Lyapunov method. Moreover, by the sliding sector method, the stability condition of switched positive fractional-order systems whose subsystems are possibly all unstable is obtained. A variable structure (VS) switching law with sliding sector is also proposed to guarantee the switched positive fractional-order system to be asymptotically stable. Finally, two numerical examples are given to demonstrate the advantages and effectiveness of our developed results.