Optimal tracking performance for SIMO systems

This paper studies the optimal tracking performance for linear time-invariant single-input multi-output (SIMO) systems responding to a step reference signal. An integral square error criterion is used as the measure of the tracking performance. First, a formula of the tracking error is derived for stable multivariable systems, which is applicable to both right-invertible and non-right-invertible cases. Then, explicit expressions of the tracking error for SIMO systems are developed. The results show that, together with the nonminimum phase zeros and unstable poles of the plant, the variation of the plant direction with frequency also contributes to the tracking difficulty in SIMO systems.