On the use of the generalized structured singular value for decentralized control problems

We study how the maximum/minimum gain of a decentralized controller influences the maximum/minimum gain of the corresponding closed loop transfer function, and provide lower bounds on the best closed-loop performance achievable by decentralized controllers satisfying additional frequency domain restrictions. These bounds are obtained using generalizations of the structured singular value and approximated by the solution of linear matrix inequalities (LMI). We close by applying our results to an active sound control problem.