A convex approach to decentralized H∞ control

We consider the design of a decentralized controller for a linear time invariant (LTI) system. This system is modeled as an interconnection of subsystems. For every subsystem, a linear time invariant controller is sought such that the overall closed loop system is stable and achieves a given H_∞ performance level. The main idea is to design every local controller such that the corresponding closed loop subsystem has a certain input output (dissipative) property. This local property is constrained to be consistent with the overall objective of stability and performance. The local controllers are designed simultaneously, avoiding the traditional iterative process: the two objectives are achieved in one shot. The application of this idea leads us to consider the following new problem: given an LTI system, parameterize all the dissipative properties which can be achieved by feedback. The proposed approach leads to solution of convex optimization problems, more precisely linear matrix inequalities