Algebraic and Differential Topology in Robust Control

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9300016 Jonckheere The proposed research is aimed at achieving a deeper understanding of the closed-loop (robust) stability issue in feedback systems under uncertain parameters. Three different directions of attack of the problem, all inspired from algebraic and differential topology, are proposed - the Simplicial Approximation Theorem, The Morse Theory, and Obstruction Theory. From there, new "simplicial" algorithms for computing the stability boundary in the space of uncertainties emerge. The general feature of these algorithms is that they are based on the idea of simplicial decomposition of the space of uncertainty. A byproduct of this approach is the elucidation of the topology of the separating boundary, bounds on the Betti numbers of the stability, and most importantly, its structural stability under perturbation of the parameters that have been declared "certain." ***