Stability robustness measures utilizing structural information

Abstract

This paper presents techniques of using weighted l₁ - and _∞ -norms to incorporate the structural information of the return difference and the perturbation matrices in the measure of stability robustness of multivariable control systems. The flexibility offered by these norms along with the use of non-negative matrix theory enables one, in most cases, to reduce the conservatism which has been a typical concern with the use of singular-value based stability robustness tests. New stability robustness criteria are derived on the basis of weighted l₁ - and _∞ -norms. Examples are given to demonstrate the merits of these methods over singular-value tests.