Study of the connexity of the set of affine controllable systems

Abstract

Purpose

This paper sets out to review a study of the set of affine controllable systems connexity denoted by C_a.

Design/methodology/approach

With each affine system a homogeneous system is associated. Jurdjevic and Sallet proved that, if a homogeneous system is controllable in R²−{0} and, if the affine system has not a fixed point, then the affine system is controllable in R².

Findings

It is shown that these systems are denoted by S, and are dense in C_a.

Research limitations/implications

Allows one to tackle the problem by using the connexity of a dense set in S.

Originality/value

Succeeds in completing a study of the set of affine controllable systems connexity denoted by C_a.

Citation

Kadem, A. (2006), "Study of the connexity of the set of affine controllable systems", Kybernetes, Vol. 35 No. 5, pp. 726-734. https://doi.org/10.1108/03684920610662476