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Robust Time and Frequency Domain Stability Analysis for Aerospace Systems

In majority of aerospace systems, time and frequency domain stability analysis with eigenvalues and gain margins are independently pursued to infer potential trajectory dispersions which contribute to design violations. In this note, it is shown that the crossover frequency computations with an uncertain loop transfer function matrix and eigenvalue analysis with a perturbed matrix superimposed on its compatible nominal stable matrix are analogous. Several examples are illustrated to show that the time and frequency domain stability analyses in this framework are indeed analogous. The computational technique applied to draw this conclusion also computes the structured singular values.