ABSTRACT The work addresses the output regulation problem for coupled linear multiple input multiple output (MIMO) hyperbolic partial integro-differential equation systems with disturbances affecting the systems through the space and boundary input. The exosystems are extended to generate ramp signals and general family of polynomial signals. The system decomposition is applied through the state transformation and yields a decoupled equivalent system. Based on the decoupled form, the backstepping transformation is applied and then in the new coordinate, the full state and output-feedback regulators are designed, respectively. For the state feedback regulator, the corresponding regulator equation is obtained and its solvability conditions are provided to facilitate the regulator design and feasibility. The design of observer-based regulator is based on the decoupling of the observer error system into a PDE subsystem and an ODE subsystem so that the backstepping approach achieves stabilisation by eigenvalue assignment leading to design of observer stabilizing gains.

中文翻译：

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一阶耦合线性MIMO双曲线PIDE系统的输出调节边界控制

摘要 这项工作解决了耦合线性多输入多输出 (MIMO) 双曲偏积分微分方程系统的输出调节问题，其中干扰通过空间和边界输入影响系统。外系统被扩展以生成斜坡信号和多项式信号的一般族。通过状态转换应用系统分解并产生解耦等效系统。基于解耦形式，应用反步变换，然后在新坐标中，分别设计全状态和输出反馈调节器。对于状态反馈调节器，得到了相应的调节器方程，并给出了其可解性条件，以方便调节器的设计和可行性。