Unknown input observer design for a class of Takagi-Sugeno descriptor systems

In this paper, we address the problem of unknown inputs observer (UIO) design for a class of nonlinear descriptor systems described by Takagi-Sugeno (T-S) structure with measurable premise variables. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the T-S descriptor model. First, the method used for separate the differential part from the algebraic part is developed. Secondly, a fuzzy observer design permitting to estimate simultaneously the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of an augmented fuzzy model which regroups the differential variables and unknown inputs. The exponential stability of the estimation error is studied by using the Lyapunov theory and the stability conditions are given in terms of LMIs. Finally, numerical simulations using a rolling disc descriptor model are given in order to highlight the performance of the proposed UIO design.

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