Design of State and Fault Observer Based on the Euler discretization for Takagi-Sugeno Implicit Models with Lipschitz constraints

摘要

In this paper, a state and fault observer design based on Euler discretization for a class of Takagi-Sugeno implicit models (TSIMs) with unmeasurable premise variables satisfying the Lipschitz constraints is proposed. Indeed, the Takagi-Sugeno (T-S) fuzzy observer design to estimate simultaneously the system state and faults in explicit form is developed. The main idea of this approach is based on the separation between dynamic and static equations of the discretized system of the TSIM. This method is developed by the construction of an augmented system regrouping the state and the actuator and sensor faults. Using the Lyapunov theory, the convergence of the state estimation error is studied and the stability condition that is given in term of only one Linear Matrix Inequalitie (LMI), the observer gain is obtained. At the end, the effectiveness of the proposal is demonstrated by using an application of TSIM of a single-link flexible joint robot.