Observer-based fractional sliding mode boundary control for coupled nonlinear reaction-subdiffusion delayed systems with input disturbances

Juan Chen, Hua-Cheng Zhou, Bo Zhuang and Ya-Juan Yu

International Journal of Systems Science, 2026, vol. 57, issue 3, 685-703

Abstract: We present sliding mode observation and output feedback fractional sliding mode control (FSM) strategy for nonlinear coupled reaction-subdiffusion systems characterised by time-fractional reaction diffusion equations under dynamic time delays, boundary disturbances and measurements. Here, system coefficients are spatially varying and distinct. First, we design an FSM observer against boundary disturbances and then prove convergence of the proposed observer via backstepping approach. An output feedback FSM observer-based controller is derived and the reaching condition to the FSM surface is established. Using fractional Lyapunov theories, delay-independent stability conditions for the controlled system are obtained. Simulations examples are stated to validate the outcome.

Date: 2026
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DOI: 10.1080/00207721.2025.2506506

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