The servomechanism problem for MIMO positive LTI systems: Switching tuning regulators and “Almost”-positivity

In this paper we consider the study of the servomechanism problem for multi-input multi-output (MIMO) linear time-invariant (LTI) positive systems. In particular, we present results on the tracking problem of nonnegative constant reference signals for unknown stable MIMO positive LTI systems with nonnegative unmeasurable constant disturbances via switching clamping control with a constraint that the control signal should be nonnegative. In addition, our results exploit the structure of tuning regulators and show that any unknown stable MIMO positive LTI system can be controlled to track any nonnegative constant reference signal while maintaining almost-positivity.