Generalized LMI observer design for discrete-time nonlinear descriptor models

The present paper provides a systematic way to generalize Takagi-Sugeno observer design for discrete-time nonlinear descriptor models. The approach is based on Finsler’s lemma, which decouples the observer gains from the Lyapunov function. The results are expressed as strict LMI constraints. To obtain more degrees of freedom without altering the number of LMI constraints and thus relax the conditions, delayed Lyapunov functions and delayed observer gains are considered. Even more relaxed results are developed by extending the approach to  -sample variation. The effectiveness of the proposed methods is illustrated via examples.