Intermittent boundary control for fixed-time stability of reaction–diffusion systems

Wenwen Jia, Jingu Xie, Haihua Guo and Yongbao Wu

Chaos, Solitons & Fractals, 2024, vol. 181, issue C

Abstract: This work is a pilot effort to investigate the fixed-time stability (FxTS) of reaction–diffusion systems under aperiodically intermittent boundary control (AIBC). The average control rate and a new Lyapunov function are proposed to overcome the challenges of handling the FxTS of reaction–diffusion systems with AIBC. Moreover, the proposed method is applicable to the study of finite-time stability and exponential stability of reaction–diffusion systems under AIBC. Based on the Wirtinger’s inequality and the Lyapunov method, a FxTS criterion for a reaction–diffusion system with AIBC is given. Finally, two examples are discussed along with the simulated results to verify the effectiveness of the proposed method.

Keywords: Fixed-time stability; Average control rate; Aperiodically intermittent boundary control; Reaction–diffusion system (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:181:y:2024:i:c:s096007792400256x

DOI: 10.1016/j.chaos.2024.114704

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