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Summary: Symmetry in the Design of Large-scale Complex
Control Systems: Some Initial Results using
Dissipativity and Lyapunov Stability
Po Wu and Panos J. Antsaklis
Abstract--In this paper, stability conditions for large-scale
systems are derived by categorizing agents into symmetry
groups and applying local control laws under limited intercon-
nections with neighbors. Particularly, stability for dissipative
systems is considered. It is assumed that subsystems are dissi-
pative and stability is studied. Conditions are derived for the
max number of subsystems that may be added while preserving
stability and these results may be used in the synthesis of large-
scale systems with symmetric interconnections.
I. INTRODUCTION
Symmetry is one basic feature of shapes and graphs. In
contrast to classical random graph models, many real-world
networks, such as the internet and US power grid, exhibit
a high degree of symmetry, resulting from the process of
tree-like or cyclic growing. The automorphism groups of
these networks can be decomposed into direct products of
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