Observer Design for a Class of Nonlinear Descriptor Systems: A Takagi-Sugeno Approach with Unmeasurable Premise Variables

Abstract

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.

Observer-based controller design for a class of Takagi-Sugeno descriptor systems

“…Theorem 2.3 [22]: The state error between the T-S descriptor model (3) and its observer (22) converges asymptotically towards zero, if there exists matrices Y 2 > 0 andỸ 2 > 0, matrices W i , i = 1, . .…”

“…However, the problems of control and observation design for nonlinear descriptor systems described by T-S models are mainly investigated in the literature. We may cite [19], [20], [21], [22], [23]. Based on a new design methodology through judicious use of the Young's inequality, the main contribution of this paper consists to propose an observerbased controller design for a class of T-S descriptor models with unmeasurable premise variables.…”

Observer design for a class of Takagi-Sugeno descriptor systems with Lipschitz constraints

“…In this section, the proposed fuzzy observer design (16) is applied to a heat exchanger pilot process in order to estimate on-line these unknown states. The following CFDS with unmeasurable premise variables that we consider here is given in [16]. It takes the form:…”

“…We may cite [8], [9], [10], [11], [12], [13]. For nonlinear descriptor systems described by T-S models, several developments exist for continuous-time case [14], [15], [16], [17] and for discrete-time one [18], [19]. Moreover, many other works dealing with observer design in explicit form called Proportional Integral Observer were also proposed for implicit T-S models.…”

Sensor Fault Diagnosis Observer for an Electric Vehicle Modeled as a Takagi-Sugeno System

“…These functions are known as weighting functions and depend on exogenous variables that can be measurable (e.g., system inputs, outputs, exogenous nonstationary parameters, velocity, and the slope of the terrain) or unmeasurable (e.g., state variables, magnetic flux, and slip angle of the tires) [12,13]. In this work, weighting functions are considered measurable.…”