On Intrinsic Geometric Stability of Controller

TL;DR

This paper develops an intrinsic geometric framework to analyze the stability and fluctuations of controllers, revealing exact correlation functions and offering a stable design approach based on geometric insights.

Contribution

It introduces a novel intrinsic geometric approach to characterize fluctuations and stability in controller configurations, including variable mismatch factors.

Findings

Exact pair correction functions derived

Global correlation volume characterized

Power fluctuations described by intrinsic geometry

Abstract

This work explores the role of the intrinsic fluctuations in finite parameter controller configurations characterizing an ensemble of arbitrary irregular filter circuits. Our analysis illustrates that the parametric intrinsic geometric description exhibits a set of exact pair correction functions and global correlation volume with and without the variation of the mismatch factor. The present consideration shows that the canonical fluctuations can precisely be depicted without any approximation. The intrinsic geometric notion offers a clear picture of the fluctuating controllers, which as the limit of the ensemble averaging reduce to the specified controller. For the constant mismatch factor controllers, the Gaussian fluctuations over equilibrium basis accomplish a well-defined, non-degenerate, flat regular intrinsic Riemannian surface. An explicit computation further demonstrates that the underlying power correlations involve ordinary summations, even if we consider the variable mismatch factor controllers. Our intrinsic geometric framework describes a definite character to the canonical power fluctuations of the controllers and constitutes a stable design strategy for the parameters.