Observer Design for Discrete-time Systems Subject to Long Time-delay

This paper addresses the problem of designing a classical observer extended to dynamical discrete-time systems with constant delays. The idea of two forms of state observers is presented to compensate fixed time-delay. Convergence conditions have been found to ensure the stability of the error dynamics and the related gains may be selected based on a set of linear matrix inequality (LMI). The results show that the compensation-based state observer is much superior in dealing with time-delay in the case that the buffer permits us to transform the time-delay system into a fixed time-delay system. Simulation and experimental results are provided to demonstrate the advantage of the proposed observation technique.