We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna–Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.

我们研究了具有恒定参考和干扰信号的不稳定适定线性无限维系统的输出跟踪和干扰抑制的样本数据控制问题。我们为存在有限维采样数据控制器（该控制问题的解决方案）提供了充分条件。为此，我们研究了无限维离散时间系统的输出跟踪和干扰抑制问题，并通过使用具有内部和边界条件的Nevanlinna-Pick插值问题的解决方案，提出了一种有限维控制器的设计方法。我们将结果应用于具有状态和输出延迟的系统。