Exploiting Structure in MIMO Scaled Graph Analysis

Abstract

Scaled relative graphs offer a graphical tool for analysis of nonlinear feedback systems. Of specific interest for stability analysis is the scaled graph, a special case of the scaled relative graph, related to non-incremental system properties. Although recently substantial progress has been made in scaled graph analysis, at present their use in multivariable feedback systems is limited by conservatism. In this paper, we aim to reduce this conservatism by introducing multipliers and exploit system structure in the analysis with scaled graphs. In particular, we use weighted inner products to arrive at a weighted scaled graph and combine this with a commutation property to formulate a stability result for multivariable feed-back systems. We present a method for computing the weighted scaled graph of Lur’e systems based on solving sets of linear matrix inequalities, and demonstrate a significant reduction in conservatism through an example.