Controllability of a class of homogeneous discrete-time bilinear systems
一类齐次离散双线性系统可控性分析

In the system analysis, controllability is an important feature of the system. In engineering practice, it is often required to discretize a continuous system. It is hoped the system after discretization to preserve important characteristics of the original system, such as controllability. For linear systems, we have a mature judgment method. However, for nonlinear systems there is no general determination method. Elliott, in 2005, gave a second-order bilinear system for which the controllability is changed after discretization. It shows that a system before and after discretization may have different controllability. We give a sufficient condition for the controllability of a class of second-order discrete bilinear system, and prove that it is more general than other existing results. Besides, we affirm that this kind of systems with orders higher than two is not controllable.