<inline-formula> <tex-math notation=LaTeX>$L_{\infty}$</tex-math> </inline-formula>-Gain of Fractional-Order Positive Systems With Mixed Time-Varying Delays

This paper investigates the Loo-gain of incommensurate fractional-order delayed positive systems (FODPSs), in which a mixture of unbounded delays and distributed delays is considered. Through the utilization of the Banach's fixed point theorem, the solution to the system is shown to exist uniquely. Then, two necessary and sufficient criteria achieving the positivity and stability of FODPSs with mixed delays are proposed, respectively. For the purpose of calculating the Loo-gain, a sample data system is formulated to approximate the lower bound of system trajectories. Additionally, it reveals that the duration of distributed delays have an impact on the Loo-gain, whereas unbounded delays will not. Finally, the validity of the theoretical results is explanted through a numerical simulation.

Automated summary

This paper investigates the Loo-gain of incommensurate fractional-order delayed positive systems (FODPSs). It proposes necessary and sufficient criteria for achieving the positivity and stability of FODPSs with mixed delays. The validity of the theoretical results is demonstrated through numerical simulation.