Synthesis of Distributed Robust H-Infinity Controllers for Interconnected Discrete Time Systems

This paper presents an algorithm for the synthesis of robust distributed controllers for interconnected linear discrete-time systems. For a network of interconnected uncertain linear time-invariant systems, the distributed controller achieves robust stability and a guaranteed level of robust performance in a well-defined H ∞ sense. The setting of this paper is in discrete time. Based on the theory of dissipative dynamical systems, conditions for the analysis of robust stability and robust performance of networks are derived in terms of feasibility tests of linear matrix inequalities. From these conditions, computationally tractable synthesis conditions are derived. An iterative D-K type of synthesis algorithm is proposed that yields a robust distributed controller. Convergence properties of the algorithm are inferred.