Distributed control of heterogeneous systems interconnected over an arbitrary graph

We consider the problem of synthesizing a distributed output-feedback controller achieving H_∞ performance for a system composed of different, interconnected sub-units, when the topology of the underlying graph is arbitrary. Using tools inspired by dissipativity theory and gain-scheduled control we derive sufficient conditions in the form of finite dimensional linear matrix inequalities. These inequalities are coupled in a way that reflects the spatial structure of the problem and in turn, can be solved using a distributed algorithm, based on alternating projections onto the different feasible sets.