Design of distributed controllers realizable over arbitrary directed networks

We consider the problem of designing stabilizing distributed output-feedback controllers that achieve H₂ and H_∞ performance objectives for a group of sub-systems dynamically interconnected via an arbitrary directed communication network. For a particular class of discrete-time linear time-invariant interconnected systems that are characterized by a structural property of their state-space matrices, we design stabilizing distributed controllers which can use the available network along with the sub-systems of the interconnected system. This is achieved by means of a parameterization for the output-feedback linear controllers that linearizes the closed-loop H₂ and H_∞ norm conditions and provide equivalent linear matrix inequalities (LMIs). Using these LMIs, we formulate the minimization of H₂ and H_∞ norms as semi-definite programs (SDPs) that can be efficiently solved using well-established techniques and tools. The solutions of these SDPs allow us to synthesize the corresponding controllers that are realizable over the given network. Even though we provide only sufficiency conditions for the design of stabilizing distributed controllers, simulations show that the synthesized controllers we obtain provide good performance in spite of being suboptimal compared to the centralized controller. In essence, we gain the advantage of designing realizable distributed controllers at the expense of slight performance degradation compared to the centralized solutions.