Optimal performance of discrete-time control systems based on network-induced delay

The optimal tracking problem for single-input single-output (SISO) linear time-invariant discrete-time systems over communication channel with network-induced delay in the feedback path is studied in this paper. The tracking performance is measured by the energy of the error response between the output of a given plant and the reference signal. An H2H2 square error criterion is used as a measure for the tracking error. The result shows that the optimal tracking performance is constrained by nonminimum phase (NMP) zeros, unstable poles of a given plant and network-induced delay. It is also shown that, if the network-induced delay of the communication channel does not exist, the optimal tracking performance reduces to the existing tracking performance of the control system without communication channel. The result obtained in this work explicitly show how the optimal tracking performance is limited by the network-induced delay. A typical example is given to illustrate the obtained theoretical results.