Large-scale systems with symmetrically interconnected subsystems: analysis and synthesis of decentralized controllers

A number of large-scale interconnected systems often encountered in practice are composed of subsystems with similar dynamics interconnected in a symmetrical fashion, and the synthesis of controllers for such systems must exploit the special structural properties in order to avoid overly conservative designs and to take advantage of the possible beneficial effects of the interconnections. An analysis of some important qualitative properties of such symmetrically interconnected systems focusing on the spectrum characterization, controllability, and observability and the solutions of the algebraic Riccati equation and the matrix Lyapunov equation are presented. Procedures for constructing the solutions to the analysis problems at the overall system level from the computationally simple subsystem level solutions are developed. A decentralized controller design procedure is presented as an illustration of the utilization of the available structural information in addressing synthesis problems. Numerical examples are included to demonstrate the superiority of the designs over existing approach which do not take full advantage of the structural knowledge of these large-scale systems