Model-based and Data-based Dynamic Output Feedback for Externally Positive Systems

In this work, we derive dynamic output-feedback controllers that render the closed-loop system externally positive. We begin by expressing the class of discrete-time, linear, time-invariant systems and the class of dynamic controllers in the space of input-output behaviors, where a dynamic controller can be expressed as a static behavioral feedback gain. We leverage the static form of the controller to derive output-feedback controllers that achieve monotonic output tracking of a constant non-negative reference output. Further, we provide a direct data-driven approach to derive monotonic tracking output-feedback controllers for single-input-single-output (SISO) systems. Our approaches, model-based and data-based, allow us to obtain output-feedback controllers that render the closed-loop system externally positive. Finally, we validate our results numerically in a drone landing control problem.