On the effect of adding frequency-response-constrained input channels on the achievable performance of discrete-time control systems

This paper deals with the effect on the control performance, of adding frequency-response-constrained control channels to a stable, discrete-time and linear time-invariant (LTI) MIMO plant. We focus on the control tracking problem with step references, in which a 2-norm based performance index is considered. In order to introduce the frequency-response limitations of the additional channels, we assume that the constraint is on the energy of the stationary deviations of the additional input signals filtered by a previously selected filter. The main result of this work is a closed form expression that quantifies the benefits on the control performance of square MIMO plants when adding input channels with those limitations.