The Takagi-Sugeno (T-S) fuzzy observer for dynamical systems described by ordinary differential equations is widely discussed in the literature. The aim of this paper is to extend this observer design to a class of T-S descriptor systems with unmeasurable premise variables. In practice, the computation of solutions of differential-algebraic equations requires the combination of an ordinary differential equations (ODE) routine together with an optimization algorithm. Therefore, a natural way permitting to estimate the state of such a system is to design a procedure based on a similar numerical algorithm. Beside some numerical difficulties, the drawback of such a method lies in the fact that it is not easy to establish a rigorous proof of the convergence of the observer. The main result of this paper consists in showing that the state estimation problem for a class of T-S descriptor systems can be achieved by using a fuzzy observer having only an ODE structure. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application to a model of a heat exchanger pilot process is given to illustrate the performance of the proposed observer.

This paper deals with the problem of the unknown inputs observer (UIO) design for nonlinear descriptor systems (NDS) described by Takagi-Sugeno (T-S) structure with unmeasurable premise variables satisfying Lipschitz conditions. The unknown inputs affect both state and output of the system. Indeed, the T-S fuzzy observer is synthesized in explicit form to estimate simultaneously the system state and the unknown inputs. The main idea of the proposed result is based on the separation between dynamic and static relations in the T-S descriptor model. Firstly, the method used to separate the dynamic equations from the algebraic equation is developed. Secondly, the fuzzy UIO design satisfying Lipschitz conditions and permitting the estimation of the unknown states and unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of the augmented fuzzy models which regroups the differential variables and unknown inputs. The convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one Linear Matrix Inequalitie (LMI). Finally, an application to a descriptor model

In this paper, we propose a new method to design an observer for a class of non linear singular systems described by Takagi-Sugeno (TS) model, with measurable decision variables. The idea of the proposed approach is based on the singular value decomposition. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in terms of Linear Matrix Inequalities (LMIs). Finally, an example is given to illustrate the proposed approach.

In this paper, we address the problem of unknown inputs observer (UIO) design for a class of nonlinear descriptor systems described by Takagi-Sugeno (T-S) structure with measurable premise variables. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the T-S descriptor model. First, the method used for separate the differential part from the algebraic part is developed. Secondly, a fuzzy observer design permitting to estimate simultaneously the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of an augmented fuzzy model which regroups the differential variables and unknown inputs. The exponential stability of the estimation error is studied by using the Lyapunov theory and the stability conditions are given in terms of LMIs. Finally, numerical simulations using a rolling disc descriptor model are given in order to highlight the performance of the proposed UIO design.

This paper presents a state and fault observer design for a class of Takagi-Sugeno implicit models (TSIMs) with unmeasurable premise variables satisfying the Lipschitz constraints. The fault variable is constituted by the actuator and sensor faults. The actuator fault affects the state and the sensor fault affects the output of the system. The approach is based on the separation between dynamic and static relations in the TSIM. Firstly, the method begins by decomposing the dynamic equations of the algebraic equations. Secondly, the fuzzy observer design that satisfies the Lipschitz conditions and permits to estimate simultaneously the unknown states, actuator and sensor faults is developed. The aim of this approach for the observer design is to construct an augmented model where the fault variable is added to the state vector. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one linear matrix inequality (LMI). Finally, numerical simulation results are given to highlight the performances of the proposed method by using a TSIM of a single-link flexible joint robot.