Observability of Perturbed Infinite-Dimensional Systems

This paper investigates the impact of compact perturbations on the exact observability of infinite-dimensional systems. The core problem is understanding how a small change (the perturbation) affects the ability to observe the system's state. The paper's significance lies in providing conditions that ensure the perturbed system remains observable, which is crucial in control theory and related fields. The asymptotic estimation of spectral elements is a key technical contribution.

• •Focuses on the observability of infinite-dimensional systems.
• •Analyzes the effect of compact self-adjoint perturbations.
• •Provides sufficient conditions for maintaining exact observability.
• •Employs asymptotic estimation of spectral elements as a key technique.