Robustness analysis of multivariable systems with time delays

A necessary and sufficient condition for robustness of linear time invariant (LTI) systems with multiple uncertain time delays in the framework of the structured singular value μ is derived. The robustness condition coupled with a transformation algorithm enables nonconservative robustness analysis to be performed on systems with multiple time delay uncertainties using existing robustness software. The stability margins for two benchmark state delay problems are exact to 4 significant figures. Further, robust performance is analyzed for a simplified paper machine model with 80 real rational parameter variations and 20 time delay uncertainties controlled by a time delay compensator.