Robust stability of time-delay systems with structured uncertainties: A μ-analysis based algorithm

This paper considers robust stability of uncertain time-delay systems affected by structured uncertainties and multiple constant delays. The objective is to compute the maximum value τ̅ the delays can reach without destabilizing the system over the uncertainty domain. A suitable modeling of the phase variations induced by the delays along the frequency range first allows to obtain an equivalent μ-analysis problem, where the bounds on some uncertain parameters depend on frequency. An algorithm is then proposed to solve this specific problem and to compute upper and lower bounds on τ̅. It is finally shown that the gap between both bounds can be reduced to any positive value in case of purely real uncertainties. The computational efficiency of the method and its ability to analyze large-scale systems are demonstrated on a numerical example, which aims at computing the MIMO time-delay margin of a high-fidelity parameter-dependent flexible aircraft model.