A geometric stabilization of planar switched systems

Cyrille Chenavier 1 Rosane Ushirobira 2 Giorgio Valmorbida 3
1 VALSE - Finite-time control and estimation for distrubed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this paper, we investigate a particular class of switching functions between two linear systems in the plan. The considered functions are defined in terms of geometric constructions. More precisely, we introduce two criteria for proving uniform stability of such functions, both criteria are based on the construction of a Lyapunov function. The first criterion is constructed in terms of an algebraic reformulation of the problem and linear matrix inequalities. The second one is purely geometric. Finally, we illustrate the second method with a numerical example.
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Cyrille Chenavier, Rosane Ushirobira, Giorgio Valmorbida. A geometric stabilization of planar switched systems. 2019. ⟨hal-02366928⟩

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