Consistent Discretization of Finite-time and Fixed-time Stable Systems

Andrey Polyakov (1) , Denis Efimov (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

Algorithms of implicit discretization for generalized homogeneous systems having discontinuity only at the origin are developed. They are based on the transformation of the original system to an equivalent one which admits an implicit or a semi-implicit discretization schemes preserving the stability properties of the continuous-time system. Namely, the discretized model remains finite-time stable (in the case of negative homogeneity degree), and practically fixed-time stable (in the case of positive homogeneity degree). The theoretical results are supported with numerical examples.

Domaines: Automatique

Andrey Polyakov, Denis Efimov, Bernard Brogliato. Consistent Discretization of Finite-time and Fixed-time Stable Systems. SIAM Journal on Control and Optimization, 2019, 57 (1), pp.78-103. ⟨10.1137/18M1197345⟩. ⟨hal-01838712v2⟩