Modified tracking performance limitations of unstable linear SIMO feedback control systems

In this paper, the optimal modified performance of the single-input multiple-output (SIMO) linear time-invariant (LTI) systems is investigated. A new modified tracking performance index is proposed to avoid the invalidity of the variance of the tracking error when the steady state tracking error is not a zero vector. The optimal modified performance is related to the scaled factor, the inner factor and the spectral density of the reference input signal. The output dimension and pole direction also play an important role in the optimal modified performance. The strong restrictions on the reference signal directions and the assumption on the plant with an integrator in the existing conclusions are not necessary. Finally, a numerical example is discussed to demonstrate the efficiency of the derived results.