Nearly-Controllable Subspaces of Discrete-Time Inhomogeneous Bilinear Systems

In this study, we investigate the nearly-controllable subspaces of a class of discrete-time inhomogeneous bilinear systems. Invertible transformations are made to bridge the inhomogeneous systems and homogeneous systems, which are used to obtain the criterion for the existence of nearly-controllable subspaces. A necessary and sufficient condition is established to derive nearly-controllable subspaces of the systems. In particular, the largest dimension of the nearly-controllable subspaces is identified, which is found to be similar with the homogeneous case. This reveals that the controllability properties of inhomogeneous systems might simply depend on their homogeneous counterparts. An example is given to illustrate the obtained results.