A Youla Operator State-Space Framework for Stably Implementable Distributed Control

This article deals with the problem of distributed control synthesis. We seek to find structured controllers that are stably implementable over the underlying network. We address the problem using an operator form of discrete-time linear systems. This allows for uniform treatment of various classes of linear systems, e.g., linear time invariant, linear time varying, or linear switched systems. We combine this operator representation for linear systems with the classical Youla parametrization to characterize the set of controllers that are implementable over the given network. Using this Youla operator state-space framework, we show that a certain separation principle holds for the distributed control of a general class of linear systems. In that, the distributed state estimation can be carried out independently and then used together with 'state-like' controllers to obtain the set of all output feedback stabilizing controllers with structure. The stability and performance problems can be formulated as convex (but infinite dimensional) optimization. We provide converging families of finite-dimensional convex optimizations in order to upper/lower approximate the original infinite-dimensional problem.