Fault/State Estimation Observer Synthesis for Uncertain T-S Fuzzy Systems

This paper studies a new approach for synthesizing an observer to estimate both unmeasurable states and faults of the T-S fuzzy system with uncertainties, simultaneously, where the bounded constraints of the uncertainties are unnecessary. Both continuous and discrete time systems are taken into account. To deal with the uncertainties and faults, first, the uncertain T-S fuzzy system is transformed into the unknown-input one; then, it is reconstructed by adding one more state equation to the system. An observer is synthesized to eliminate completely the effects of the uncertainties and estimate the unknown states and faults, simultaneously. The fuzzy Lyapunov function is employed to relax the observer design conditions. On the basis of the Lyapunov theory and the linear matrix inequality technique, the conditions for observer design are derived in the main theorems. Finally, an illustrative example is introduced for both continuous and discrete time systems to prove the effectiveness of the proposed method.