Design of Exponentially Stabilizers for Distributed Control Systems Subject to Cyber Disconnections

Distributed control architectures are attractive for large-scale interconnected systems as they provide good trade-offs between control complexity and closed-loop performance. In such a context, it becomes crucial to ensure robustness against variations in the communication topology arising from connectivity failures or cyber-attacks. Based on Linear Matrix Inequalities, this paper introduces a novel design approach for distributed controllers that exhibit robustness to changes in the communication topology. The primary objective is to achieve resilience against potential disconnections of subsystems that may occur within the communication network. The control gains are structured, and reflect the nominal communication topology. Exponential stability with a prescribed decay rate is guaranteed within the sub-configurations of the nominal communication topology. The proposed approach does not make any assumptions regarding the connectivity of the communication graph. Moreover, leveraging on the projection lemma, the design of control gains is decoupled from the design of the Lyapunov matrix, thus minimizing the conservativeness of the solution. An illustrative example on a multimachine power system is presented to demonstrate the effectiveness of the proposed approach.