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

Localization of Control Synthesis Problem for Large-Scale Interconnected System Using IQC and Dissipativity Theories