This paper investigates the design problem of observers for nonlinear descriptor systems described by Takagi-Sugeno (TS) system; Depending on the available knowledge on the premise variables two cases are considered. First a TS descriptor system with measurables premises variables are proposed. Second, an observer design which satisfying the Lipschitz condition is proposed when the premises variables are unmeasurables. 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). Examples are included to illustrate those methods.
The present paper attempts to investigate the problem of Fault Tolerant Control for a class of uncertain neutral time delay systems. In the first time, we consider an additive control that is based on adding a term to the nominal law when the fault occurs. This approach will be designed in three steps. The first step is fault detection while the second one is fault estimation. For these two steps, we consider the adaptive observer to guarantee the detection and estimation of the fault. The third step is the fault compensation. Lyapunov method and Linear Matrix Inequality (LMI) techniques were considered to improve the main method. Second, we propose a Pseudo Inverse Method "PIM" and determine the error between the closed loop and the nominal system. Finally, simulation results are presented to prove the theoretical development for an example of an uncertain neutral time delay system.
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