Applied Lyapunov Stability on Output Tracking Problem for a Class of   Discrete-Time Linear Systems
  The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a reference model. By using the solution of the Lyapunov equation, the convergence of the tracking error to the origin, is proved. The proposed approach employs linear controllers rather than nonlinear ones. Therefore, the designing method is simple for use and the resulting controller is easy to implement. An application of the proposed approach for a class of perturbed systems is also considered. Finally, numerical examples are given to demonstrate the validity of the results. 
Omar Zakary, Mostafa Rachik
cs.SY math.AP math.OC