An LMI approach to dencentralized H-infinity control

We consider the design of a decentralized controller for a linear time inva riant (LTI) system. This system is modelled as an interconnection of subsys tems. For every subsystem, a linear time invariant controller is sought suc h that the overall closed loop system is stable and achieves a given H-infi nity performance level. The main idea is to design every local controller s uch that the corresponding closed loop subsystem has a certain input-output (dissipative) property. This local property is constrained to be consisten t with the overall objective of stability and performance. The local contro llers are designed simultaneously, avoiding the traditional iterative proce ss: both objectives (the local one and the global one) are achieved in one shot. Applying this idea leads us to solving the following new problem: giv en an LTI system, parameterize all the dissipative properties which can be achieved by feedback. The proposed approach leads to solving convex optimiz ation problems that involve linear matrix inequality constraints.