Title :
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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2010.2072551
