This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in Francis (1997) and Isidori and Byrnes (1990). We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system.
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机译：在参考信号和扰动是由有限维外生系统产生的情况下，这项工作将输出调节的几何理论扩展到具有有限输入和输出算子的线性分布参数系统。特别地，表明，在且仅当一对调节器方程式可解的情况下，在稳定性和可检测性的标准假设下，全状态反馈和误差反馈调节器问题是可解决的。对于线性分布参数系统，这代表了Francis（1997）和Isidori and Byrnes（1990）发展的输出调节几何理论的扩展。我们还基于外部系统的特征值和系统传递函数，为调节器方程的可解性提供了简单的标准。给出了抛物线系统的周期性跟踪，设定点控制和干扰衰减以及阻尼双曲线系统的周期性跟踪的示例。
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