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This article investigates the problem of fuzzy boundary (FB) control for nonlinear second-order hyperbolic partial differential equation systems (HPDESs) with time-varying delay (TVD). Considering the existence of TVD that widely appears in actual HPDESs, the presented FB control approach is more practical and effectively reduces the control cost, requiring few actuators and sensors in comparison with the fuzzy distributed control method. Initially, one can obtain a fuzzy model of the nonlinear delayed second-order HPDES by utilizing Takagi–Sugeno (T–S) fuzzy modeling technology. Subsequently, by using the Lyapunov direct approach, sufficient conditions for the exponential stability (ES) of closed-loop nonlinear delayed HPDES based on spatial linear matrix inequality (SLMI) are derived. Then, the FB control design issue of nonlinear delayed second-order HPDES is expressed as an LMI feasibility issue. Lastly, the provided FB control approach is validated by the simulation results.
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Zhang et al. (2025) studied this question.
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