A general framework for analysing robust synchronization in large-scale heterogenous networks is proposed based on the theory of integral quadratic constraints (IQCs). Dynamic agents are represented as linear time-invariant single-input-single-output systems. The agents exchange information according to a sparse dynamical interconnection operator in order to achieve synchronization, where their outputs are steered to the same, possibly time-varying, signal. The main technical hindrance to applying IQCs in this context lies with the presence of the marginally stable dynamics which define the trajectory to which the agents' outputs synchronize. It is shown that by working with conditions defined on modified signal spaces of interest and exploiting the graph structure underlying the connections between the dynamic systems, IQC methods can be applied directly to synchronization analysis without recourse to loop transformations, which may obscure the inherent structural properties of the multi-agent networked systems. Decentralized and scalable conditions for synchronization are proposed within this setting. The IQC framework is demonstrated to unify and generalize some of the existing results in the literature, including certain Nyquist-type consensus certificates for time-delay systems. Moreover, it allows the role of feedback in robustness against uncertainty to be better manifested within the context of synchronization.
Bibliographical noteFunding Information:
This work was partially supported by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation and the Swedish Research Council through the LCCC Linnaeus Centre. Recommended by Associate Editor G. N. Nair.
© 1963-2012 IEEE.
- distributed analysis
- heterogeneous multi-agent networks
- integral quadratic constraints