From the introduction: “The motivation for this paper stems from a desire to characterize the robustness properties of sampled-data (SD) control systems. Such systems are invariably time-varying, but often the time-variation is periodic. As such, the approach taken here is to study linear, periodically time-varying (LPTV) feedback systems.
The paper has the following structure. In section 2, the notation, terminology and preliminary mathematics used throughout the paper are introduced. Section 3 is devoted to the gap matric, with the main result being a formula for the directed gap between two LPTV systems. In section 4, quantitative robustness results are obtained in terms of the gap metric. The main result characterizes the largest gap-ball of LPTV plants centered at a nominal plant that a nominal stabilizing LPTV controller is guaranteed to stabilize. In addition to this, robustness to simultaneous gap-perturbations of both the nominal plant and the controller is considered. To conclude this section, the main robustness result is specialized to SD control systems in which the sampling and hold devices are synchronized and periodic.”
This paper is nicely written and notably its introduction is an example of clarity. This is really how introductions should be!