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Pré-Publication, Document De Travail Année : 2008

Plane geometry and convexity of polynomial stability regions

Résumé

The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and Bezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.
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Dates et versions

hal-00206129 , version 1 (16-01-2008)

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Didier Henrion, Michael Sebek. Plane geometry and convexity of polynomial stability regions. 2008. ⟨hal-00206129⟩
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