Robust Control of Systems Consisting of Symmetrically Interconnected Subsystems

This paper is concerned with robust control of systems consisting of n similar interacting subsystems. The transfer function matrices for these systems are block circulant matrices. For H¿, optimal control, we show that we can to simplify controller synthesis by considering two systems of the same dimension as the subsystems instead of the overall system. This leads to a dramatic reduction in system size for system consisting of many subsystems, and we are able to optimize the H¿ criterion in n directions, as opposed to standard H¿ synthesis which only optimizes the criterion in the worst direction. The structured singular value, ¿, is shown to be independent of the structure of the uncertainty for cases with SISO subsystems and only one uncertainty block. For MIMO systems or cases with several uncertainty blocks, we are able to reduce the plant size from n · no × n · ni to a block diagonal plant with diagonal blocks of size no × ni (for subsystems of dimension no × ni) if we assume all the uncertainty blocks to be full.