Linear time invariant homogeneous matrix descriptor (singular) discrete-time systems with non consistent initial conditions

Several applications in mechanics, in engineering, as well as, in financial issues, have been benefited by the use of digital computers. Thus, in the literature of system and control theory, the discrete-time systems gain-ed a special merit. In this paper, we discuss the solution properties of a very interesting class of descriptor systems. So, we provide with the solution of linear time invariant homogeneous matrix descriptor (singular) discrete-time systems with non-consistent initial conditions. The lack of consistency to the initial conditions makes the problem more general and too far challenging. Consequently, using the properties of ztransform, the solution is fully discussed and provided.