On the enhancement of high-gain observers for state estimation of nonlinear systems

International audienceAn enhanced high-gain observer is proposed to estimate the state variables of dynamic systems with Lipschitz nonlinearities. Such an observer has a more general structure as compared with the standard high-gain observer, which can be regarded as a particular case of enhanced high-gain observer because of a special choice of the design parameters. The more general structure allows for additional degrees of freedom in the selection of the observer parameters, which however entails some difficulties in the design. To overcome such difficulties, a convenient design procedure is presented that is based on the use of the Young inequality and linear matrix inequalities. Numerical results are reported to evaluate the effectiveness of the proposed observer and its related design tools as compared with the high-gain observer

A new LMI condition for decentralized observer-based control of linear systems with nonlinear interconnections

International audienceThis paper presents a new decentralized observer-based stabilization scheme for a class of nonlinear interconnected systems. A novel Linear Matrix Inequality (LMI) condition is proposed to ensure the asymptotic stability. This improved LMI is established thanks to the use of the well known Young inequality in a judicious manner. Beside the use of such an inequality, we introduce some additional degrees of freedom which allow to furtherly relax the LMI. Based on the aforesaid, an application of the proposed LMI approach to the design of controllers that are both robust and resilient is presented. Numerical examples are presented in order to demonstrate the validity of our method

State observer design method for a class of non-linear systems

In this study, the authors develop a new high-gain observer design method for non-linear systems. This new design provides a lower gain compared to both the high-gain and the enhanced high-gain observer. The idea is to combine the improved high-gain methodology with the linear matrix inequality based observer design technique to build a more general observer that allows one to exploit the benefits of both approaches. A numerical example is given to show the effectiveness of the proposed observer with different values of the Lipschitz constant and of the compromise index

High-Gain Nonlinear Observer Using System State Augmentation

This paper deals with the problem of state estimation of dynamic systems with Lipschitz nonlinearities using a new high gain observer design. The aim of this new design procedure is to reduce the value of the tuning parameter and the observer gain compared to the standard high gain observer on the one hand without solving a set of LMIs as in the LMIbased observer on the other hand. Towards this end, a novel approach based on system state augmentation that transforms the original system of dimension n into a new system whose dimension is (n + js), where the new nonlinear function does not depend on js last components of the new state. A numerical example is reported to evaluate the effectiveness of the proposed observer for different values of the Lipschitz constant