Performance limitations in tracking of linear system with measurement noise

An optimal performance issues about linear time-invariant (LTI) systems tracking stochastic signal with measurement noise is proposed in this paper. An integral square error criterion is used as a measure for the system tracking error between the output of a given plant and reference signals, the spectral factorization is applied to obtain optimal solution of the system error. It is shown that nonminimum phase zeros and unstable poles have a negative effect on a feedback system´s ability to reduce the system error with measurement noise; simultaneously, the performance limitation becomes worse for an unstable, nonminimum phase plant because of measurement noise. Finally, the measurement noise don´t affect performance limitation for an stable nonminimum phase plant.