On Synthesis of Stabilizing Distributed Controllers with an Application to Power Systems

This paper presents synthesis results for distributed controllers for interconnected linear time-invariant systems. The setting of the paper is in discrete time. A parameterization of the closed-loop system is used for interconnected systems and distributed static state feedback controllers with an interconnection structure that can be chosen arbitrary in the design phase. Based on conditions for closed-loop stability using centralized static state feedback, computationally tractable synthesis procedures are derived that yield a distributed controller. The synthesis procedures involve convex optimization problems in the form of linear matrix inequalities (LMIs) which are solved in a centralized way. Suggestions are made to reduce the number of independent variables in the problems. An algorithm is presented that uses these synthesis procedures to find a controller with a distributed structure or eliminates candidate controller structures using heuristics. A complexity analysis for the synthesis procedures is incorporated. The synthesis algorithm is illustrated on examples of electric power systems, proving feasibility of the synthesis procedures for real-life applications.