On Uncontrollable Discrete-Time Bilinear Systems Which are "Nearly" Controllable

作者：Tie Lin^*; Cai Kai Yuan; Lin Yan

来源：IEEE Transactions on Automatic Control, 2010, 55(12): 2853-2858.

DOI：10.1109/TAC.2010.2072551

• Controllable region
• cyclicity
• discrete-time bilinear systems
• hypersurface
• Jacobian determinant
• near-controllability
• sign patterns

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 [1] are generalized to arbitrary finite-dimensional cases.

• 单位
  北京大学