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

Author

Listed:
  • Bai, Zhiye
  • Wu, Baowei
  • Wang, Yue-E
  • Qiu, Hongling

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.

Suggested Citation

  • Bai, Zhiye & Wu, Baowei & Wang, Yue-E & Qiu, Hongling, 2026. "Stability analysis of fractional-order cone-invariant systems with distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 558-570.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:558-570
    DOI: 10.1016/j.matcom.2025.07.016
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