This article presents a new control design strategy for stabilising large-scale interconnected systems operating in semi-automatic control modes. The large-scale system is modelled by subsystems connected to each other in an arbitrary configuration. Each subsystem is regulated by a dedicated multivariable controller that also allows for a manual control mode. The notion of asymptotically positive realness constraint (APRC) is introduced and applied for deriving the interconnection stabilisability condition in the time domain. The interactions between subsystems are taken into consideration in the stability condition. The APRC is subsequently employed in the so-called stabilising agent to accommodate the closed-loop control and man-in-the-loop coexistence. The multipliers of the APRC quadratic supply rate are updated on-the-fly to ensure that the constraint satisfaction of stabilising agents is recursively feasible. The stabilising agents are developed independently from the control law under the same auspice controller. Due to this independence, operational errors from the manual control adjustments, that may destabilise the control systems, can be avoided. The decentralised agents render stabilising bounds for the manipulated variables in the automatic control mode, and at the same time, provide warning signals and manipulation guidance for the operators to prevent possible plant-wide destabilisation in the manual control mode. Our main results are illustrated through numerical simulations for an industrial modular system.