分数阶时滞锥不变系统的稳定性和增益性能OA

This paper mainly studies the stability and input-output gain of fractional-order linear systems with cone invariance and unbounded time-varying delays.The trajectories of such systems are usually restricted in a proper cone,which is a generalization of fractional-order delayed positive systems.Firsly,using the trajectory of the solution of the system state equation,a necessary and sufficient condition that ensures the cone invariance of the system is given.According to the partial order relationship on a proper cone,a necessary and sufficient condition that ensures the asymptotic stability of fractional-order cone-invariant delayed system is given.The method is also applicable to the case when the system without delays,which means that the stability of fractional-order cone-invariant systems is not sensitive to the size of delays.Moreover,through the construction of a sampling system using rounding functions and the analysis of the partial order relationship between state trajectories of the sampling system and their corresponding counterparts without delays,the cone-induced gain of fractional-order cone-invariant systems is characterized in terms of system matrices.Finally,a numerical example is provided to illustrate the theoretical results.