Graph-Theoretic Methods for Networked Dynamic Systems: Heterogeneity and H2 Performance

  • Daniel Zelazo
  • Mehran Mesbahi


The analysis and synthesis of large-scale systems pose a range of challenges due to the number of their subsystems and the complexity of their interactions. In the meantime, the importance of these systems has become increasingly prevalent in science and engineering, especially in the realm of multi-agent systems such as coordination of autonomous vehicles on ground, in sea, air, and space, as well as localization and sensor fusion, energy networks, and distributed computation [1,2,4–7,9,19,21]. One aspect of the complexity of large-scale systems is that their subsystems, which we occasionally refer to as `agents,` may not be described by the same set of inputoutput dynamics. The difference between the dynamics of distinct subsystems may be the result of manufacturing inconsistencies or intentional differences due to varying requirements for each subsystem in the ensemble. An important component to the analysis of these systems, therefore, is to understand how heterogeneity in the subsystem dynamics affects the behavior and performance of the entire system. Another facet of this complexity relates to the interconnection of different subsystems. The underlying interconnection topology of a large-scale system may be determined by the governing dynamic equations of each subsystem, e.g., when the interconnection is a function of some state of each subsystem, or it may be designed as part of the engineering process. In both cases, the interconnection topology has a profound impact on the overall system in terms of its stability, controllability, observability, and performance.


Span Tree Optimal Topology Minimum Span Tree Incidence Matrix Consensus Model 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute for Systems Theory and Automatic ControlUniversity of StuttgartStuttgartGermany
  2. 2.Department of Aeronautics and AstronauticsUniversity of WashingtonWashingtonUSA

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