On the impact on MIMO zeros and achievable performance of adding additional input channels to square MIMO discrete-time systems

This paper studies the impact of adding additional control channels to a square discrete-time MIMO plant. Our aim is to quantify the performance gains and therefore, to determine whether this benefit, compared to the cost associated to the channels implementation and maintenance, is such as to justify the additional channels. We first analyse the impact on the non-minimum phase zeros (including zeros at infinity) when we add input channels. Then, we compute the associated change on the best achievable performance, as measured by a quadratic index. We compute explicit expressions for the difference between the best achievable performance in the control of the original square and the resulting fat systems. As expected, our results show that the impact of adding input channels is related to the non-minimum phase zeros that are removed as a consequence of adding additional input channels.