On Uncontrollable Discrete-Time Bilinear Systems Which are “Nearly” Controllable

Author

Tie, Lin ; Cai, Kai-Yuan ; Lin, Yan

Author_Institution

Sch. of Autom. Sci. & Electr. Eng., Beijing Univ. of Aeronaut. & Astronaut., Beijing, China

Volume

55

Issue

12

fYear

2010

Firstpage

2853

Lastpage

2858

Abstract

In this note, for a class of uncontrollable discrete-time bilinear systems, it is shown that the controllable region “nearly” covers the whole space while the uncontrollable region is only a hypersurface. As a result, for almost any initial state and any terminal state of the system, the former can be transferred to the latter. In addition, the two-dimensional controllability counterexamples in are generalized to arbitrary finite-dimensional cases.

Keywords

Jacobian matrices; bilinear systems; control nonlinearities; controllability; discrete time systems; multidimensional systems; Jacobian determinant; controllable region; finite dimensional case; initial state; terminal state; two dimensional controllability; uncontrollable discrete time bilinear system; uncontrollable hypersurface region; Controllability; Discrete time systems; Eigenvalues and eigenfunctions; Jacobian matrices; Nonlinear systems; Controllable region; Jacobian determinant; cyclicity; discrete-time bilinear systems; hypersurface; near-controllability; sign patterns;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2072551

Filename

5560745