Distributed robustness analysis of heterogeneous networks via integral quadratic constraints

• Published in: 2015 American Control Conference (ACC) pp. 3980 - 3985
• Main Authors: Sei Zhen Khong, Rantzer, Anders
• Format: Conference Proceeding
• Language: English
• Published: American Automatic Control Council 01.07.2015
• Subjects: Additives; chordal graphs; Distributed robustness analysis; Feedforward neural networks; integral quadratic constraints; Interconnected systems; Matrix decomposition; Robustness; Uncertainty
• ISSN: 0743-1619; 2378-5861
• DOI: 10.1109/ACC.2015.7171951

Robust performance of networks of interconnected heterogenous nonlinear dynamic systems is studied using the theory of integral quadratic constraints. By appealing to recent results on chordal sparsity decompositions of rational transfer matrices, distributed and scalable certificates for performance of interconnections are proposed. The approach is more direct since it does not involve reformulating the problem in terms of standard closed-loop configurations as is typical in the literature, which may destroy or conceal the structural properties inherent in the interconnections. The well-studied notion of feedback performance is reinvestigated within this framework. It is shown that feedback performance can be verified in a distributed fashion if the signal variables in the feedback interconnection are selected appropriately. Another contribution of the paper lies in identifying three chordality-preserving operations that are standard in control and modelling theory, namely local feedback, feedforward, and additive input-output perturbations.