Linear Regulator-based synchronization of positive discrete-time multi-agent systems

A fundamental challenge in control theory is designing protocols that achieve synchronization in interconnected systems. This paper addresses positive synchronization on undirected graphs for homogeneous discrete-time positive systems. It introduces a static feedback protocol derived from the Linear Regulator problem, where the stabilizing policy is determined by solving an algebraic equation using a linear program. Furthermore, necessary and sufficient conditions are established to guarantee the positivity of each agent’s trajectory for all nonnegative initial conditions. The proposed approach is demonstrated through simulations on large regular graphs with varying nodal degrees, illustrating its effectiveness.