Decentralized Control of Complex Systems: Lyapunov Function Approach

In this contribution, we generalize existing methods for decentralized control design, providing a unified methodological framework that applies to linear continuous and discrete-time complex systems, as well as certain classes of nonlinear complex systems. Our approach leverages the direct connection between the stability properties of the overall complex system and those of its individual subsystems. By conducting the entire controller design process at the subsystem level, we circumvent the need for explicit interconnection values. Through numerical examples, we demonstrate that the proposed method ensures asymptotic stability of the full complex system within a specified region, and also guarantees stability of the isolated subsystems. In particular, we obtain quantifiable stability margins (e.g., gamma c bounds) and closed-loop eigenvalue placements that verify the effectiveness of the design. These results highlight not only the method's theoretical robustness, but also its practical significance in simplifying the design process, reducing computational overheads, and enhancing scalability for large and interconnected engineering systems.