Large-Scale Dissipative and Passive Control Systems and the Role of Star and Cyclic Symmetries

In this technical note, symmetries in large-scale dissipative and passive control systems are considered. In the framework of dissipativity and passivity theory, stability conditions for large-scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors. Building upon previous studies on stability of (Q,S,R)- dissipative large-scale systems, we show that for cyclic and star-shaped symmetric systems there exists an upper bound on the number of subsystems that can be added to preserve stability of dissipative systems. In cyclic and star-shaped symmetric systems, the subsystems can be heterogeneous as long as they satisfy the same dissipative inequalities. Approximate symmetry with respect to interconnections is also considered and the robustness of the results is demonstrated.

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