A geometric stabilization of planar switched systems

Cyrille Chenavier (1) , Rosane Ushirobira (1) , Giorgio Valmorbida (2, 3, 4)

1 VALSE - Finite-time control and estimation for distributed systems
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 L2S - Laboratoire des signaux et systèmes
4 CentraleSupélec

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.

Mots clés: algebraic approaches; geometric approaches; stabilization; switching functions; Linear systems

Domaines: Systèmes dynamiques [math.DS]

Cyrille Chenavier, Rosane Ushirobira, Giorgio Valmorbida. A geometric stabilization of planar switched systems. IFAC 2020 - 21st IFAC World Congress, Jul 2020, Berlin, Germany. ⟨10.1016/j.ifacol.2020.12.1787⟩. ⟨hal-02366928v2⟩