Sufficient condition for stability of decentralized control feedback structures

We consider the problem of achieving stability for large-scale systems by decentralized diagonal control feedback structures. For this problem, a sufficient condition is proposed such that by satisfying this condition, overall stability of a large scale system is guaranteed by a decentralized diagonal controller; this controller is obtained from the set of controllers stabilizing the system consisting of the diagonal entries of the original system. More specifically, our sufficient condition is in terms of the H^∞ norm of the closed loop diagonal transfer function matrix and the structured singular value (μ) of the off-diagonal state matrix of the system. Furthermore, by an example, we show that our sufficient condition is less conservative than the one proposed by Grosdidier and Morari (1986)