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

Yuanhong Ren, Xiangning Yuan, Dingli Hua, Guanghui Zhang and Mingxuan Shen

Chaos, Solitons & Fractals, 2026, vol. 202, issue P2

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.

Keywords: Input-state stability; Infinite-dimensional system; Lyapunov function (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015772

DOI: 10.1016/j.chaos.2025.117564

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