The Multivariable Servomechanism Problem for Positive LTI Systems

In this technical note we study the servomechanism problem for positive open-loop stable LTI systems under constant tracking signals and constant disturbances. In particular, we show that in general the MIMO servomechanism problem for positive systems is not solvable, but is solvable for various classes of MIMO systems, and for the class of SISO systems in which the disturbances are small compared to the tracking signal. In particular, we give existence results as to what subclass of reference and disturbance signals can be considered, for the case when either the mathematical model of the plant is known or unknown, and we provide the controller structure that solves the problem for the case of measurable or unmeasurable disturbance signals.