Stability of Infinite-dimensional Sampled-data Systems with Unbounded Control Operators and Perturbations

TL;DR

This paper investigates the robustness of exponential stability in infinite-dimensional sampled-data systems with unbounded control operators, demonstrating that small Desch-Schappacher perturbations do not compromise stability.

Contribution

It provides a novel analysis showing that exponential stability is preserved under small unbounded perturbations in infinite-dimensional sampled-data systems.

Findings

Exponential stability is robust against small Desch-Schappacher perturbations.

Stability preservation is established for systems with boundary perturbations.

Results apply to systems modeled by partial differential equations.

Abstract

We analyze the robustness of the exponential stability of infinite-dimensional sampled-data systems with unbounded control operators. The unbounded perturbations we consider are the so-called Desch-Schappacher perturbations, which arise, e.g., from the boundary perturbations of systems described by partial differential equations. As the main result, we show that the exponential stability of the sampled-data system is preserved under all Desch-Schappacher perturbations sufficiently small in a certain sense.