An LMI approach to dencentralized H8 control

Abstract

We consider the design of a decentralized controller for a linear time invariant (LTI) system. This system is modelled 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: 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: given an LTI system, parameterize all the dissipative properties which can be achieved by feedback. The proposed approach leads to solving convex optimization problems that involve linear matrix inequality constraints.