The function space to describe the dynamics of linear systems

TL;DR

This paper proposes a new function space framework for describing linear system dynamics, resolving contradictions in traditional models and improving noise mitigation methods, with applications to aircraft automatic landing systems.

Contribution

It introduces a shift to almost periodic function spaces for linear systems, addressing inconsistencies and enhancing noise reduction techniques.

Findings

Elimination of contradictions in linear system descriptions.

Development of a new noise mitigation method.

Successful application to aircraft automatic landing data.

Abstract

Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to contradictions. It is shown that the transition to the Hilbert space of almost periodic functions leads to the elimination of the detected inconsistencies. Multiple signals and interference with discrete spectrum are systems of sets. The properties of these systems lead to a new more effective method to combat noise in this space. The method used to identify the differential equations for the airbus. Baseline data were obtained during automatic landing.