Finite-Time and Fixed-Time Observer Design: Implicit Lyapunov Function Approach

Francisco Lopez-Ramirez (1) , Andrey Polyakov (1) , Denis Efimov (1) , Wilfrid Perruquetti (1)

1 NON-A-POST - Non-Asymptotic estimation for online systems

This work deals with the problem of finite-time and fixed-time observation of linear multiple input multiple output (MIMO) control systems. The proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed (defined a priori) time. Algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out. The theoretical results are illustrated by numerical examples that consider both noisy and noise-free measurements and a comparison with a high-gain observer is included.

Mots clés: Finite-Time Stability; Fixed-Time Stability; Implicit Lyapunov Function; Homogenous Systems

Domaines: Automatique

Francisco Lopez-Ramirez, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. Finite-Time and Fixed-Time Observer Design: Implicit Lyapunov Function Approach. Automatica, 2018, 87, pp.52 - 60. ⟨10.1016/j.automatica.2017.09.007⟩. ⟨hal-01622356⟩