On Consistent Discretization of Finite-time Stable Homogeneous Differential Inclusions

Andrey Polyakov (1) , Bernard Brogliato (2)

1 VALSE - Finite-time control and estimation for distributed systems
2 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses

This paper deals with the problem of consistent discretization of the generalized homogeneous differential inclusions which appear, in particular, as mathematical models of many sliding mode systems. An algorithm of consistent implicit discretization for homogeneous finite-time stable system is developed. It preserves the finite-time stability property and reduces the numerical chattering. The scheme is demonstrated for the so-called "nested" second order sliding mode algorithm.

Mots clés: Sliding Modes; Digital Implementation; Lyapunov Methods

Domaines: Automatique

Andrey Polyakov, Bernard Brogliato. On Consistent Discretization of Finite-time Stable Homogeneous Differential Inclusions. 2020. ⟨hal-02514847⟩