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Stabilization analysis of diagonal infinite-dimensional systems with bounded distributed delays

Author

Listed:
  • Ren, Yuanhong
  • Yuan, Xiangning
  • Hua, Dingli
  • Zhang, Guanghui
  • Shen, Mingxuan

Abstract

This study investigates the exponential input-state stability for diagonal infinite-dimensional systems with constant delays and bounded distributed delays. The feedback control strategy is constructed in two steps. First, the initial infinite-dimensional system is truncated by spectral decomposition to obtain a finite-dimensional subsystem. In this subsystem, a controller is designed for the finite-dimensional time delay system by using Artstein transformation and displacement theorem, so as to capture the unstabilized part of the infinite-dimensional system. Second, an appropriately selected Lyapunov functional is utilized to ensure that the controller, developed for the finite-dimensional delay system, is capable of stabilizing the original infinite-dimensional system with delays, thereby guaranteeing exponential input-to-state stability for the resulting closed-loop dynamics. Finally, we verify the validity of the theoretical results by an example analysis.

Suggested Citation

  • Ren, Yuanhong & Yuan, Xiangning & Hua, Dingli & Zhang, Guanghui & Shen, Mingxuan, 2026. "Stabilization analysis of diagonal infinite-dimensional systems with bounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015772
    DOI: 10.1016/j.chaos.2025.117564
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