On almost decentralized stabilization problem

In the problem of decentralized stabilization the objective is to internally stabilize a system of N channels by a constrained feedback in which no information transfer is allowed from the output channel i to the input channel j unless i=j. In this paper we consider a similar problem where the "no information exchange" constraint among the local controllers is relaxed to a "weak information exchange" constraint. Specifically, in the almost decentralized stabilization problem, we determine the conditions for the existence of a stabilizing controller transfer matrix of arbitrarily small H/sub /spl infin// norm at its block off-diagonal entries. It turns out that if the system satisfies a new type of connectivity condition (which is milder than the condition of strong connectedness), then almost decentralized stabilization is possible. If this connectivity condition fails, then with this type of weak information exchange among local controllers, one can only remove the imaginary axis poles of the system.