Improving observer design for discrete-time TS descriptor models under the quadratic framework

The paper presents a new quadratic Lyapunov function for observer design for discrete-time nonlinear descriptor systems. The main idea is to represent the original nonlinear model as a Takagi- Sugeno one and then use Lyapunov's direct method to design the observer. The well-known Finsler's Lemma is used to design a non-Parallel-Distributed-Compensator-like observer together with a quadratic Lyapunov function. This procedure yields design conditions in terms of linear matrix inequalities. The effectiveness of the proposed approaches is illustrated via numerical examples.