  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.
