A new approach to fault detection observer design of nonlinear time-delay systems via fuzzy Lyapunov functions

This paper addresses the design problem of fault detection (FD) observer for nonlinear systems via Takagi-Sugeno(TS) fuzzy model approach. By employing a new fuzzy Lyapunov function and several slack variables, the stability and H_- index fault sensitivity conditions for TS fuzzy models with time-delay are established. The analyzing results provide an efficient technique to reduce the conservatism in stability analysis and H_- index estimation. Some new sufficient conditions for the existence of fuzzy FD observer gains of the time-delay system are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical example is given to show the effectiveness of the proposed approach.