Stability analysis of fractional-order cone-invariant systems with distributed delays

Zhiye Bai, Baowei Wu, Yue-E Wang and Hongling Qiu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 558-570

Abstract: This article addresses the problem of stability and gain analysis for fractional-order cone-invariant systems subjected to time-varying distributed delays. Depending on the Banach fixed point theorem, the system’s solution is demonstrated to exist uniquely. Subsequently, a necessary and sufficient criterion is deduced to guarantee the cone invariance of delayed systems using a fractional differential operator. By combining the partial order relation on proper cones with the inductive reasoning, the asymptotic stability of fractional-order cone-preserving systems with distributed delays is demonstrated, with stability conditions that are equivalent to those of systems with constant delays. Furthermore, an explicit representation of cone-induced gain is put forward for cone-invariant systems in the presence of delays via utilizing the comparison principle, revealing that the cone-induced gain depends on the duration of the distributed delays. Finally, numerical simulations are performed to verify the rationality of the obtained results.

Keywords: Fractional-order system; Cone invariance; Distributed delay; Stability (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:558-570

DOI: 10.1016/j.matcom.2025.07.016

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