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.
Highlights
The control and the supervision of a process require the knowledge of the state of the process
We are concerned with the problem of the observer synthesis for nonlinear descriptor systems that can be described by dynamic models of T-S descriptor with unmeasurable premise variables
The T-S fuzzy observer problems for dynamic T-S fuzzy models described by ordinary differential equations (ODEs) with measurable and unmeasurable premise variables are studied in [10–20]
Summary
The control and the supervision of a process require the knowledge of the state of the process. In many cases and due to a high running cost and physical constraints, this method becomes very limited To solve this problem, one solution is to design an observer. The T-S fuzzy observer problems for dynamic T-S fuzzy models described by ordinary differential equations (ODEs) with measurable and unmeasurable premise variables are studied in [10–20]. Concerning nonlinear descriptor systems described by T-S descriptor models the problem of fuzzy observer design has been widely investigated; see, for instance, [21–25]. The aim of this paper is to give a fuzzy observer design to a class of fuzzy descriptor systems permitting to estimate the unknown state without the use of an optimization algorithm. The method used for decomposing the differential part of the algebraic part is developed; secondly we give a fuzzy observer design permitting to estimate the unknown state.
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