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Research Paper#Control Theory, Observability, Infinite-Dimensional Systems🔬 ResearchAnalyzed: Jan 3, 2026 06:34

Observability of Perturbed Infinite-Dimensional Systems

Published:Dec 31, 2025 18:37
1 min read
ArXiv

Analysis

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.
Reference

“The paper derives sufficient conditions on a compact self adjoint perturbation to guarantee that the perturbed system stays exactly observable.”

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Research Paper#Graph Theory, Network Analysis, Signal Processing🔬 ResearchAnalyzed: Jan 4, 2026 00:07

Harmonic Analysis for Directed Networks

Published:Dec 25, 2025 19:36
1 min read
ArXiv

Analysis

This paper addresses the challenges of analyzing diffusion processes on directed networks, where the standard tools of spectral graph theory (which rely on symmetry) are not directly applicable. It introduces a Biorthogonal Graph Fourier Transform (BGFT) using biorthogonal eigenvectors to handle the non-self-adjoint nature of the Markov transition operator in directed graphs. The paper's significance lies in providing a framework for understanding stability and signal processing in these complex systems, going beyond the limitations of traditional methods.
Reference

“The paper introduces a Biorthogonal Graph Fourier Transform (BGFT) adapted to directed diffusion.”

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