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Optimization over Polynomials for Analysis of Polynomial Vector Fields

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Polynomial Optimisation

We present complexity results and semidefinite programming (SDP) based algorithms for stability analysis of polynomial differential equations. We show that deciding asymptotic stability of homogeneous cubic vector fields is strongly NP-hard. We then settle some of the converse questions on existence of polynomial and sum of squares Lyapunov functions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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