Convex Reformulation of LMI-Based Distributed Controller Design with Non-Block-Diagonal Lyapunov Functions

This study presents novel convex LMI-based methods for designing distributed state feedback controllers for continuous-time linear time-invariant systems using a class of non-block-diagonal Lyapunov functions. The proposed approach generalizes the conventional block-diagonal relaxation and provides necessary and sufficient conditions for distributed controllers under chordal communication graphs.