The Robust Exact Differentiator Toolbox: Improved Discrete-Time Realization

This paper presents a new release of A Robust Exact Differentiator Toolbox for Matlab®/Simulink® proposed in [1]. This release features a new discrete-time realization of the continuous-time robust exact differentiator. The implemented discretization scheme is less sensitive to gain overestimation and does not suffer from the discretization chattering effect. Hence, the single tuning parameter of the new version of the implemented differentiator is more intuitive to tune. Furthermore, it shows superior estimation performance in the case of large sampling times in comparison to the previous release. This is confirmed by the presented results obtained by numerical simulations and a real world application

A Consistent Discretisation method for Stable Homogeneous Systems based on Lyapunov Function

International audienceIn this paper we propose a discretisation scheme for continuous and asymptotically stable homogeneous systems. This method is based on the dynamics of the system projected on a level surface of a homogeneous Lyapunov function. The discretisation method is explicit and preserves the convergence rate of the continuous-time system

Lyapunov-based Consistent Discretisation of Stable Homogeneous Systems

International audienceIn 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

Discrete-time differentiators: design and comparative analysis

This work deals with the problem of online differentiation of noisy signals. In this context, several types of differentiators including linear, sliding-mode based, adaptive, Kalman, and ALIEN differentiators are studied through mathematical analysis and numerical experiments. To resolve the drawbacks of the exact differentiators, new implicit and semi-implicit discretization schemes are proposed in this work to suppress the digital chattering caused by the wrong time-discretization of set-valued functions as well as providing some useful properties, e.g., finite-time convergence, invariant sliding-surface, exactness. A complete comparative analysis is presented in the manuscript to investigate the behavior of the discrete-time differentiators in the presence of several types of noises, including white noise, sinusoidal noise, and bell-shaped noise. Many details such as quantization effect and realistic sampling times are taken into account to provide useful information based on practical conditions. Many comments are provided to help the engineers to tune the parameters of the differentiators