In this paper, a tractable sampled-data controller synthesis method is proposed for linear time-invariant plants that gives guarantees for stability and performance of the closed-loop system in terms of the ${\mathcal{H}}_{\infty }$- and ${\mathcal{H}}_2$-norm. This is done by taking a so-called jump/hybrid systems approach, which allows formulating linear matrix inequalities using an explicit solution to the Riccati differential equation. Furthermore, the sampled-data problem is formulated such that continuous-time design techniques like ${\mathcal{H}}_{\infty }$ loop-shaping can be used in a sampled-data context. To do so, it is essential to consider mixed discrete/continuous specifications, in which both discrete and continuous signals are weighted using weighting filters. This leads to a generalised plant that has both continuous-time and discrete-time dynamics. The controller design method is demonstrated on a benchmark example, in which we compare to existing results in the literature, and on a design example of reference tracking of a two-mass–spring–damper system.

本文提出了一种线性时不变设备的易于处理的采样数据控制器综合方法，该方法为闭环系统的稳定性和性能提供了保证。 ${\mathcal{H}}_{\infty }$-和 ${\mathcal{H}}_2$-规范。这是通过采用所谓的跳跃/混合系统方法完成的，该方法允许使用Riccati微分方程的显式解来公式化线性矩阵不等式。此外，制定了采样数据问题，以使诸如${\mathcal{H}}_{\infty }$循环整形可用于采样数据上下文中。为此，必须考虑混合的离散/连续规范，其中使用加权滤波器对离散信号和连续信号进行加权。这导致具有连续时间和离散时间动态的广义工厂。控制器设计方法在一个基准示例中进行了演示，在该示例中我们将与文献中的现有结果进行比较，并在一个双质量弹簧减振器系统的参考跟踪的设计示例中进行了演示。