Feedback Regulation for Irreducible Max-Plus Linear Systems

This letter proposes the feedback regulation of max-plus linear systems, and designs the regulator for irreducible systems that ensures the system can directly enter a uniform periodic steady state, regardless of the initial input. The feedback regulator configures the period and transient of the system to become 1. Moreover, it preserves the eigenvalues and eigenvectors of the original system. The proposed method is constructive and has polynomial complexity. The feedback regulation approach is applied in manufacturing systems to streamline operations and improve consistency.