On output feedback control of positive linear systems

This note is concerned with stabilization and optimal control for state space systems that exhibit the so-called “internal positivity” property. Specifically, we generalize the results by A. Rantzer (IEEE CDC 2011, p.6008-6011) to the multiple-input-multiple-output setting, and show that a stabilizing decentralized output feedback controller that makes the closed-loop system internally positive and satisfying a general quadratic performance index, when it exits, can be computed using linear programming. An example related to decentralized control of a vehicle platoon is examined to illustrate the proposed synthesis conditions.