We give an overview of a technique for analysing the performance of large dynamical networks, such as electrical power systems. The technique can be used to guarantee that a certain level of performance is achieved by the network on the basis of a set of low complexity decentralised tests. These tests are robust to structural changes within the network, and can also be used to guide the design of local control systems. The conditions are used to demonstrate that the oscillatory modes within a benchmark power system model are sufficiently well damped. The analysis is then extended to provide the same guarantees for power systems models of arbitrary size.