  The synthesis problem for the compositional performance certification of
interconnected systems is considered. A fairly unified description of control
synthesis problem is given using integral quadratic constraints (IQC) and
dissipativity. Starting with a given large-scale interconnected system and a
global performance objective, an optimization problem is formulated to search
for admissible dissipativity properties of each subsystems. Local control laws
are then synthesized to certify the relevant dissipativity properties.
Moreover, the term localization is introduced to describe a finite collection
of syntheses problems, for the local subsystems, which are a feasibility
certificate for the global synthesis problem. Consequently, the problem of
localizing the global problem to a smaller collection of disjointed sets of
subsystems, called groups, is considered. This works looks promising as another
way of looking at decentralized control and also as a way of doing performance
specifications for components in a large-scale system.
