Distributed Robust Stability Analysis of Interconnected Uncertain Systems

TL;DR

This paper presents a distributed method for robust stability analysis of large interconnected uncertain systems using integral quadratic constraints, enabling efficient and conservative-free analysis through decomposed linear matrix inequalities.

Contribution

It introduces a novel distributed approach that decomposes the stability analysis problem into smaller LMIs, maintaining equivalence to the original problem without added conservativeness.

Findings

Efficient distributed stability analysis for large networks.

Decomposition maintains problem equivalence and conservativeness.

Applicable to interconnected uncertain systems with sparse interconnections.

Abstract

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.