Structural controllability and structural near-controllability of a class of discrete-time bilinear systems

In this paper, we consider the structural controllability problems of a class of driftless discrete-time bilinear systems which have nearly the same structure as linear systems. Algebraic as well as graph-theoretic conditions for structural controllability of such systems with single-input and multi-input are, respectively, obtained. Furthermore, we introduce a new notion, called structural near controllability, for those structured systems which cannot be structurally controllable but structurally nearly-controllable. It is shown that the bilinear systems can be structurally nearly-controllable although their linear counterparts can never have a large controllable region no matter what the parameters are chosen. Necessary and sufficient conditions for structural near-controllability of the bilinear systems are thus derived. We also consider the structural controllability problem in the continuous-time case. Examples and graphs are given to illustrate the obtained results of this paper.