Rebarber, Richard (Univ. of Nebraska-Lincoln), Townley, Stuart (Univ. of Exeter)

Sampled-Data Control of Infinite-Dimensional Systems: Recent Advances and Open Problems

Scheduled for presentation during the Mini-Symposium "Distributed Parameter Systems-V: Optimization and Numerical Implementation" (FrA06), Friday, July 28, 2006, 10:25−10:50, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

This paper is in three parts. 1. An overview of sampled-data control for infinite-dimensional systems including: fundamental necessary conditions which must hold for stabilisation by sampled-data control to be possible; notions of open-loop stabilization and stabilization by generalised hold; robustness vs. non-robustness of continuous-time static/dynamic feedback stabilisation with respect to sufficiently small sampling times. 2. Some recent results on generalised-hold sampled-data stabilisation of well-posed linear systems and robustness of continuous-time state feedback stabilisation of Riesz spectral systems with respect to sampling. 3. An overview of `Open Problems in Sampled-data Control for Infinite Dimensional Systems'. In the `robustness with respect to sampling' context there is a gap between the necessary conditions for sampled-data stabilization and the known sufficient conditions. We will explore the limitations of the existing results and ideas for ways forward. The analysis of this fundamental problem emphasises how an approach that mixes state-space and input-output approaches is needed in the sampled-data setting. We llustrate our results using PDE examples.