Strong Stability of Sampled-data Riesz-spectral Systems

TL;DR

This paper investigates the strong stability of sampled-data systems derived from Riesz-spectral infinite-dimensional systems, establishing conditions under which stability is preserved for sufficiently small sampling periods.

Contribution

It provides new conditions ensuring the strong stability of sampled-data Riesz-spectral systems when sampling is sufficiently fast.

Findings

Strong stability is preserved under fast sampling for Riesz-spectral systems.

The paper extends the Arendt-Batty-Lyubich-Vu theorem to sampled-data stability analysis.

Conditions are identified under which the sampled-data system remains strongly stable.

Abstract

Suppose that a continuous-time linear infinite-dimensional system with a static state-feedback controller is strongly stable. We address the following question: If we convert the continuous-time controller to a sampled-data controller by applying an idealized sampler and a zero-order hold, will the resulting sampled-data system be strongly stable for all sufficiently small sampling periods? In this paper, we restrict our attention to the situation where the generator of the open-loop system is a Riesz-spectral operator and its point spectrum has a limit point at the origin. We present conditions under which the answer to the above question is affirmative. In the robustness analysis, we show that the sufficient condition for strong stability obtained in the Arendt-Batty-Lyubich-V\~u theorem is preserved between the original continuous-time system and the sampled-data system under fast sampling.