[2603.01076] Feasible Pairings for Decentralized Integral Controllability of Non-Square Systems

Mathematics > Optimization and Control arXiv:2603.01076 (math) [Submitted on 1 Mar 2026] Title:Feasible Pairings for Decentralized Integral Controllability of Non-Square Systems Authors:Yuhao Tong, Steven W. Su View a PDF of the paper titled Feasible Pairings for Decentralized Integral Controllability of Non-Square Systems, by Yuhao Tong and 1 other authors View PDF HTML (experimental) Abstract:This paper investigates the determination of feasible input-output pairings for the decentralized integral controllability of non-square systems. The relevance of this problem extends beyond traditional industrial processes into modern AI research, particularly Multi-Agent Reinforcement Learning (MARL), where environments frequently act as strongly non-square mappings that evaluate high-dimensional joint action spaces via comparatively low-dimensional global rewards. To address the stability of these complex distributed architectures, we extend the concept of D-stability to non-square matrices, providing a crucial mathematical foundation. We formally define D-stability for non-square matrices as a direct generalization of the square case. By introducing the concept of ``Squared Matrices'', which are derived from specific column selections of the non-square formulation and directly correspond to candidate control pairings, we establish a fundamental link between the stability of these square sub-components and the original non-square system. Ultimately, we propose sufficient conditio...