Optimal modified tracking performance of linear SIMO systems for the step signal

In this paper, the optimal modified performance of the single-input multiple-output (SIMO) linear time-invariant (LTI) systems for the step signal is investigated. A new modified performance index is proposed by introducing the scaled factor. The assumption on the limited scaled factor is discussed. The performance bound is related to the scaled factor, the inner factor and the direction of the reference signal. The output dimension also plays an important role. The strong restrictions on the directions of the reference signal and the assumption that the plant must have an integrator in the existing conclusions are not necessary. Also the modified performance index overcomes the invalidity when the state error is not zero vector. Two examples are given to verify the efficiency of the results derived.