Static output-feedback stabilization with optimal L1-gain for positive linear systems

This paper is concerned with the static output-feedback stabilization with optimal L1-gain for positive linear systems. We aim to construct a static output-feedback controller such that the closed-loop system is positive, asymptotically stable and the L1-gain from the exogenous input to the regulated output is minimized. We show that when the control input or the measured output is a scalar, this problem can be directly solved via linear programming by adding a one dimensional search. Moreover, it is pointed out that the results can be extended to solve the L∞-optimal controller synthesis problem. Finally, several illustrative examples are given to show the effectiveness of the theoretical results.