Foliation Theory and it's applications

TL;DR

This paper reviews foliation theory results and explores its applications in control systems, emphasizing smoothness in $C^ abla$ class, and presents both theoretical foundations and practical implications.

Contribution

It provides a comprehensive review of foliation theory and demonstrates its application in the qualitative analysis of control systems.

Findings

Foliation theory results are summarized and extended.

Applications in control systems are systematically analyzed.

The paper emphasizes smoothness in $C^ abla$ class for theoretical consistency.

Abstract

Subject of present paper is the review of results of authors on foliation theory and applications of foliation theory in control systems. The paper consists of two parts. In the first part the results of authors on foliation theory are presented, in the second part the results on applications of foliation theory in the qualitative theory of control systems are given. In paper everywhere smoothness of a class $C^\infty$ is considered.