Lyapunov-based Consistent Discretisation of Stable Homogeneous Systems

Tonametl Sanchez (1) , Andrey Polyakov (2) , Denis Efimov (2)

1 IPICYT - Instituto Potosino de Investigacion Cientifica y Tecnologica
2 VALSE - Finite-time control and estimation for distributed systems

In this paper we propose a discretisation scheme for asymptotically stable homogeneous systems. This scheme exploits the information provided by a homogeneous Lyapunov function of the system. The main features of the scheme are: 1) the dis-cretisation method is explicit and; 2) the discrete-time system preserves the asymptotic stability, the convergence rate, and the Lyapunov function of the original continuous-time system.

Mots clés: Nonlinear systems; homogeneous systems; Lyapunov-based methods; discrete-time systems

Domaines: Automatique

Tonametl Sanchez, Andrey Polyakov, Denis Efimov. Lyapunov-based Consistent Discretisation of Stable Homogeneous Systems. International Journal of Robust and Nonlinear Control, 2020, ⟨10.1002/rnc.5308⟩. ⟨hal-02972714⟩