控制理论与应用2026，Vol.43Issue(3)：471-479,9.DOI:10.7641/CTA.2024.40177
分数阶时滞锥不变系统的稳定性和增益性能
Stability and gain performance of fractional-order delayed cone-invariant systems
摘要
Abstract
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.关键词
分数阶正系统/锥不变性/锥诱导增益/无界时滞Key words
fractional-order positive system/cone invariance/cone-induced gain/unbounded delays引用本文复制引用
邱宏凌,沈俊..分数阶时滞锥不变系统的稳定性和增益性能[J].控制理论与应用,2026,43(3):471-479,9.基金项目
国家自然科学基金项目(61973156),江苏省研究生科研与实践创新计划项目(KYCX24_0593)资助.Supported by the National Natural Science Foundation of China(61973156)and the Postgraduate Research & Practice Innovation Program of Jiangsu Province(KYCX24_0593). （61973156）
