Stability multipliers and mu upper bounds: Connections and implications for numerical verification of frequency domain conditions

The main contribution of the paper is to show the equivalence between the f ollowing two approaches for obtaining sufficient conditions for the robust stability of systems with structured uncertainties: 1) apply the classical absolute stability theory with multipliers and 2) use modern it theory, spe cifically, the mu upper bound obtained by Fan et al. [11], In particular, t he relationship between the stability multipliers used in absolute stabilit y theory and the scaling matrices used in the cited reference Is explicitly characterized. The development hinges on the derivation of certain propert ies of a parameterized family of complex linear matrix inequalities (LMI's) , a result of independent interest. The derivation also suggests a general computational framework for checking the feasibility of a broad class of fr equency-dependent conditions, based on which bisection schemes can be devis ed to reliably compute several quantities of interest for robust control.