A Global High-Gain Finite-Time Observer

Abstract

A global finite-time observer is designed for nonlinear systems which are uniformly observable and globally Lipschitz. This result is based on a high-gain approach combined with recent advances on finite-time stability using Lyapunov function and homogeneity concepts.

Homogeneous approximations and local observer design

“…According to Theorem 2.1 in [13], in the the new coordinates z dened by the inverse of the function 20) where…”

“…Explicit constructions for nonlinear systems have been investigated, for example high gain observers (see [8,9,16,20]) or backstepping observers (see [2,19]). But these constructions only apply to very specic class of systems.…”

Fixed-time observer with simple gains for uncertain systems

“…Another alternative is to design nite-time observers using as simple gains as the one obtained in the linear case. This track has accomplished considerable progress [32,38,27]. Other observers with time varying gains or additional assumptions have been developed in [37,39,25,26].…”

A high-gain-based global finite-time nonlinear observer

“…For example, (Perruquetti et al 2008) introduces a finite-time observer with application to secure communication, where a homogeneous Lyapunov function is constructed. Then, based on this homogeneous Lyapunov function, semi-global finite-time and two different kinds of global finite-time observers are designed for single output triangular nonlinear systems which are uniformly observable and globally Lipschitz (Shen and Xia 2008), (Shen and Huang 2009), (Ménard et al 2010). Global finite-time observers ) are proposed for a class of globally Lipschitz nonlinear systems with nontriangular structure where the interactions between all the states of the nonlinear terms are allowed.…”