An LMI approach for structured ℋ∞state feedback control

In this paper we consider the problem of designing optimal ℋ∞ static state feedback control in the presence of structural constraints on the feedback gain. This problem arises in many applications, such as Network Decentralized Control and Overlapping Control, where the controller is constrained to have a specific nonzero patterns. Building upon previous results on S-variable approach for LMI-based robust control, we derive a novel solution to the design of ℋ∞ state feedback controllers when the controller gain is constrained to belong to a given linear space. Through numerical examples we demonstrate the simplicity of the method and performance of the optimal control law.