Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition

TL;DR

This paper introduces a chordal decomposition-based distributed method for robust stability analysis of large interconnected uncertain systems, reducing computational complexity and preserving privacy.

Contribution

It proposes a novel decomposition scheme based on system interconnection structure that enables distributed analysis without added conservativeness.

Findings

Efficient distributed analysis without centralization

No additional conservativeness introduced by the decomposition

Numerical experiments demonstrate effectiveness

Abstract

Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.