Control Limits A Structural Characterisation of Intervention Failure in Admissible Systems

This paper introduces Control Limits within the Paton System as a structural characterisation of when intervention fails to maintain system admissibility. Building on Admissibility Control and Control Cost the framework defines control limits as conditions under which admissibility cannot be preserved regardless of intervention. These limits arise from structural constraints in admissible space including vanishing admissibility margin inaccessible trajectories prohibited basin transitions and diverging control cost. The approach provides a domain independent method for identifying the boundary of controllability and recognising when stabilisation is no longer possible without modifying underlying governing equations.