Distributed Controller Design for Discrete-Time Systems Via the Integration of Extended LMI and Clique-Wise Decomposition

This study addresses a distributed controller design problem for discrete-time systems using linear matrix inequalities (LMIs). Sparsity constraints on control gains of distributed controllers result in conservatism via the convexification of the existing methods such as the extended LMI method. In order to mitigate the conservatism, we introduce a novel LMI formulation for this problem, utilizing the clique-wise decomposition method from our previous work on continuous-time systems. By reformulating the sparsity constraint on the gain matrix within cliques, this method achieves a broader solution set. Also, the analytical superiority of our method is confirmed through numerical examples.