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Stability and Performance of Large Networks: In many networks maintaining performance independent of size is essential. For example a power system must maintain its operating frequency and voltage as consumers join and leave the grid. I am interested in how to design a network to have this property.
My PhD thesis was concerned with the above, where we demonstrated that provided the building blocks of an (electrical) network are interconnected in a particular way, the network inherits the designed properties of each piece (stability, l2 gain, etc). We use this approach to show how, for example, stability of an electrical power system with many generating areas can be deduced from one with two.