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This letter describes a method for estimating regions of attraction andbounds on permissible perturbation amplitudes in nonlinear fluids systems. Theproposed approach exploits quadratic constraints between the inputs and outputsof the nonlinearity on elliptical sets. This approach reduces conservatism andimproves estimates for regions of attraction and bounds on permissibleperturbation amplitudes over related methods that employ quadratic constraintson spherical sets. We present and investigate two algorithms for performing theanalysis: an iterative method that refines the analysis by solving a sequenceof semi-definite programs, and another based on solving a generalizedeigenvalue problem with lower computational complexity, but at the cost of someprecision in the final solution. The proposed algorithms are demonstrated onlow-order mechanistic models of transitional flows. We further compare accuracyand computational complexity with analysis based on sum-of-squares optimizationand direct-adjoint looping methods.

Estimating Regions of Attraction for Transitional Flows using Quadratic Constraints