Robust State-Coupled Fault Estimation Based on Observer Design for Lipschitz Nonlinear Systems With State Disturbance Using Polytopic Linear Model

This article aims to design observers for the purpose of simultaneously estimating the fault and states of a class of Lipschitz nonlinear systems and attenuating the effect of disturbances. Fault and disturbance are considered as nonlinear functions coupled with the states of the system. To estimate a fault coupled with the states, two observers are designed separately. In the first method, the nonlinear function of the fault is represented by a polytopic linear model (PLM) with unmeasurable premise variables. Also, based on the dissipativity theory, the effect of disturbance can be attenuated using Lipschitz matrix. To declare the conditions for the existence of the proposed observer, the Lyapunov method and S-Procedure Lemma are used through the linear matrix inequality (LMI) formulation. Then in the second method, fault and states of system are estimated by designing an observer and considering an
$\boldsymbol{\varepsilon }$
-accurate PLM with bounds on Taylor remainder. The second approach is able to increase the feasibility of the design and the accuracy of fault estimation. However, the main advantage of the first method is that it has less computational complexity compared to the second method. The efficiency of the proposed methods has been validated by the simulation of an Electro-pump system subject to fault and disturbance both coupled with the system states.