Symmetry in the Design of Large-Scale Complex Control Systems: Some Initial Results Using Dissipativity and Lyapunov Stability

In this paper, stability conditions for large-scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors. Particularly, stability for dissipative systems is considered. It is assumed that subsystems are dissipative 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.