Observers Design for Takagi-Sugeno Models

Abstract

In this paper, the problem of state and unknown input estimation for nonlinear systems described by Takagi-Sugeno models is studied. The considered systems are affected by actuator and sensor faults. Thanks to the use of a mathematical transformation, an augmented system is conceived in which all the faults affecting the initial system appear as unknown inputs. A proportional multiple integral observer (PMI) and a proportional integral observer with unknown inputs (PIUI) are proposed in order to estimate the state and the faults. The convergence of the estimation errors between the system and each observer are formulated in linear matrices inequalities.. Academic examples are provided in order to illustrate the proposed methods. A comparison between the two observers is applied to mobile robot.