ABSTRACT This paper investigates the design problem of collocated feedback controllers for a class of semi-linear distributed parameter systems with mixed time delays. The spatially distributed is divided by a finite number of intermittently local actuators and sensors. In order to deal with the problem of exponential stability analysis, the framework of a class of novel interval Lyapunov functional is established. By utilising Schur complement and linear matrix inequality (LMI) techniques, the corresponding stabilisation condition is then derived. Furthermore, the robust control problem is considered for the uncertain distributed parameter systems with external load disturbance and mixed time delays. Based on the feedback controller, the exponentially stability condition is derived for the uncertain systems. Finally, the simulation examples are presented to show the effectiveness of the proposed feedback control approach for Fisher equation and Blake–Scholes option pricing model.

中文翻译：

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一类具有混合时滞的半线性抛物线分布参数系统的反馈控制

摘要 本文研究了一类具有混合时滞的半线性分布参数系统的并置反馈控制器的设计问题。空间分布由有限数量的间歇性局部执行器和传感器划分。为解决指数稳定性分析问题，建立了一类新的区间Lyapunov泛函的框架。通过利用 Schur 补和线性矩阵不等式 (LMI) 技术，然后推导出相应的稳定条件。此外，考虑了具有外部负载扰动和混合时滞的不确定分布参数系统的鲁棒控制问题。基于反馈控制器，推导出不确定系统的指数稳定性条件。最后，