L2L2 optimal decentralised static output feedback stabilisation of a network of dynamical systems

In this paper global L2L2  stabilisation of a network of dynamical systems is attained by local decentralised static output feedback control. The proposed synthesis procedure guarantees an upper bound on the achievable L2L2  performance in the presence of disturbances. The synthesis of such a controller is posed as an iterative LMI optimisation problem. The algorithm is guaranteed to achieve a local minimum as a result of the iterations. The synthesis of the controller is independent of the number of nodes in the network and depends only on the size of the node level dynamics. A randomly generated academic example with 12 nodes is considered to demonstrate the efficacy of the proposed methodology.