The Analysis of Robust Stability and Performance in Multivariable Feedback Systems using M-Matrices

A new technique for the analysis of robust stability and performance in multivariable feedback systems is presented. Structured plant uncertainties are considered, and strict bounds are placed on the frequency reponse of the closed loop. A scalar measure of robustness is derived using M-matrices, and it is shown to be scale invariant. The criterion may be used to synthesize filters for the IMC control configuration. An additional scalar measure, similar to a condition number, is introduced which describes the relative sensitivity of a plant transfer matrix to modeling error.