Design of fuzzy observer for a class of Takagi-Sugeno descriptor systems subject to unknown inputs

This paper considers the problem of the unknown input observer design of a class of Takagi-Sugeno fuzzy descriptor models with measurable premise variables. The unknown inputs affect both state and output of the system. Based on the singular value decomposition approach, a new observer design in explicit structure is developed to estimate simultaneously the system state and the unknown inputs. More precisely, the proposed approach is based on the synthesis of an augmented fuzzy model which regroups the state 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 linear matrix inequalities (LMIs). Finally, an application to a Takagi-Sugeno fuzzy descriptor model of a rolling disc process is presented to show the validness of the proposed approach.