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

TL;DR

This paper presents a novel LMI-based approach with clique-wise decomposition to design distributed controllers for discrete-time systems, reducing conservatism and expanding feasible solutions compared to traditional methods.

Contribution

The paper introduces a new LMI formulation incorporating clique-wise decomposition for distributed control design, enhancing solution flexibility and reducing conservatism.

Findings

Broader solution set achieved with the new LMI formulation.

Numerical examples confirm the analytical advantages of the proposed method.

Reduced conservatism compared to existing extended LMI approaches.

Abstract

This study addresses the centralized synthesis of distributed controllers 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.