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On robust control algorithms for nonlinear network consensus protocols. (English) Zbl 1185.93108

Summary: Even though many consensus protocol algorithms have been developed over the last several years in the literature, robustness properties of these algorithms involving nonlinear dynamics have been often ignored. Robustness here refers to sensitivity of the control algorithm achieving semistability and consensus in the face of model uncertainty. In this paper, we examine the robustness of several control algorithms for network consensus protocols with information model uncertainty of a specified structure. In particular, we develop sufficient conditions for robust stability of control protocol functions involving higher-order perturbation terms that scale in a consistent fashion with respect to a scaling operation on an underlying space with the additional property that the protocol functions can be written as a sum of functions, each homogeneous with respect to a fixed scaling operation, that retain semistability and consensus of the system.

MSC:

93D09 Robust stability
93A14 Decentralized systems
93C10 Nonlinear systems in control theory
34H05 Control problems involving ordinary differential equations
93C41 Control/observation systems with incomplete information
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