Decentralized H∞ controller design:: An LMI approach

This paper considers decentralized H-infinity controller design problems for multi-channel linear time-invariant systems. Our interest is focused on dynamic output feedback, and our discussion concerns both continuous-time systems and discrete-time ones. The decentralized H-infinity control problems axe expressed as feasibility problems of bilinear matrix inequalities (BMIs) with respect to variables of a coefficient matrix defining the controller and a Lyapunov matrix. To deal with the BMIs, we propose to set the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller so that the BMIs are reduced to. linear matrix inequalities (LMIs) which are sufficient to the BMIs but much more tractable.