A Linear Matrix Inequality for Robust Stability Analysis with Frequency-Dependent Multipliers

In this paper we introduce a linear matrix inequality (LMI) condition for robust stability analysis. The condition is expressed as a pair of convex inequalities that provides an upper bound for the structured singular that can be used to verify stability and performance robustness. This robust analysis test incorporates a particular class of frequency-dependent multipliers and can be limited to finite frequency intervals, features which can significantly reduce conservatism as compared to existing conditions with similar complexity. The results are illustrated with a simple numerical example that illustrates the improvement of the proposed LMI condition