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<p>The present paper studies the boundary stabilization problem for a class of uncertain 1-dim reaction-diffusion systems(RDS) with state-delay by using sliding mode control(SMC) approach. The system model simultaneously contains time-varying state delay and disturbance resulted from both internal domain and boundary. The proposed sliding variable only depends on the boundary point state. Correspondingly, the resulting boundary sliding mode control(BSMC) law only requires the boundary state accessibility. Compared with BSMC law depending on full-domain states, the proposed BSMC law is easier to implement. The sufficient conditions for exponential stability of sliding motion are provided through the linear matrix inequality(LMI) approach. The proposed BSMC law has continuality to avoid annoying chattering of sliding mode, and it can realize reachability of sliding mode. Finally, a numerical simulation is given to test the effectiveness of the proposed results.</p>

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Continuous Sliding Mode Boundary Stabilization of Uncertain Reaction Diffusion Systems With Time-Varying State Delay

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • B. Kao,
  • Hailong Xing,
  • Fule Li

摘要

The present paper studies the boundary stabilization problem for a class of uncertain 1-dim reaction-diffusion systems(RDS) with state-delay by using sliding mode control(SMC) approach. The system model simultaneously contains time-varying state delay and disturbance resulted from both internal domain and boundary. The proposed sliding variable only depends on the boundary point state. Correspondingly, the resulting boundary sliding mode control(BSMC) law only requires the boundary state accessibility. Compared with BSMC law depending on full-domain states, the proposed BSMC law is easier to implement. The sufficient conditions for exponential stability of sliding motion are provided through the linear matrix inequality(LMI) approach. The proposed BSMC law has continuality to avoid annoying chattering of sliding mode, and it can realize reachability of sliding mode. Finally, a numerical simulation is given to test the effectiveness of the proposed results.