Robust synchronization problems for max-plus linear systems with polytopic uncertainties

In this paper, the robust system synchronization problems for max-plus linear systems with polytopic uncertainties affecting all system matrices are addressed. Uncertainties in discrete event systems can arise from variations in timing constraints or processing delays. This work provides a methodology to tackle synchronization problems by leveraging a geometric approach in the algebraic max-plus framework. Solution methods aim to synthesize a control law to make the system replicate a reference model, forcing the system's output to equal the model's output. An illustrative example supports the proposed theoretical results.