Discrete-time lifting via implicit descriptor systems

This paper introduces a new representation for the parameters of the discrete-time lifted plants. In this representation the lifted parameters are expressed as discrete-time dynamic systems in the implicit descriptor form. We argue that the operations over these dynamic systems can effectively be performed in the state-space, in terms of the original plant parameters. Consequently, the computational efficiency of the discrete-time lifting technique is improved, and the structures of the original problems can easily be recovered from their lifted solutions. The efficiency of the proposed approach is demonstrated through the investigation of the discrete-time algebraic Riccati equation associated with a discrete-lifted system.