Stability Analysis of Perturbed Infinite-dimensional Sampled-data Systems

TL;DR

This paper investigates the stability of infinite-dimensional sampled-data systems under unbounded perturbations, demonstrating conditions under which exponential stability is preserved by analyzing semigroup continuity.

Contribution

It introduces two classes of unbounded perturbations that maintain exponential stability, advancing understanding of stability in infinite-dimensional sampled-data systems.

Findings

Identifies classes of unbounded perturbations that preserve stability.

Establishes the continuity of semigroups with respect to generators.

Provides theoretical conditions for stability preservation.

Abstract

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this end, we investigate the continuity of strongly continuous semigroups with respect to their generators, considering the uniform operator topology.