Proportional Tracking Control of Positive Linear Systems

This letter considers the reference tracking of positive linear systems via a proportional controller, which remains an open problem. Through using a virtual reference method in state-space models, optimal tracking performance is guaranteed for single-input multi-output (SIMO) systems via a bisection method. The proportional tracking for multi-input multi-output (MIMO) systems is reformulated as a bi-convex programming problem and a convergence-guaranteed algorithm is developed through using iterative linear matrix inequalities. Numerical simulations are provided to verify the proposed results.