Design of unknown inputs and multiple integral observers for Takagi-Sugeno multiple model

In this paper, a proportional multiple integral observer (PMI) and a proportional integral observer with unknown inputs (PIUI) are proposed in order to estimate the state, the actuator and the sensor faults of nonlinear systems described by a Takagi-Sugeno multiple model. The convergence of the estimation errors between the system and each observer are studied using the Lyapunov theory. Academic examples are provided in order to illustrate the proposed methods. A comparaison between the two observers is made through mobile robot.