Performance bounds for SIMO and squared-up plant models

This paper presents performance bounds in the control of SIMO plant models, and the variation of those bounds when input channels are added to the plant so as to make it square. Our work focuses on discrete-time, linear time invariant (LTI) MIMO systems, minimizing the squared regulation error when an impulsive input disturbance is injected into the plant. Closed form expressions for the optimal regulation performance are developed, and the sensitivity of the performance to channel addition is also investigated. Finally, a numerical example is presented to illustrate the main results of the paper.