Qualitative analysis and decentralized controller synthesis for a class of large-scale systems with symmetrically interconnected subsystems

Abstract

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 focussing on the spectrum characterization, controllability and observability, and the solutions of the algebraic Riccati equation and the matrix Lyapunov equation is conducted in this paper and procedures for constructing the solutions to the analysis problems at the overall system level from the computationally simple subsystem level solutons 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 presented designs over the use of existing approaches which do not take full advantage of the structural knowledge in these large-scale systems.