Fuzzy observer design using linear matrix inequalities for fuzzy closed-loop control systems

Linear observers play an important role in modern control theory and practice. A systematic design method of fuzzy observers would be important for fuzzy control as well. The fuzzy observer is designed by solving linear matrix inequalities (LMI) that represent control performance such as disturbance rejection and robust stability. Our approach in designing the fuzzy observer is based on the LMI formulation of the stability conditions for closed-loop Takagi-Sugeno (T-S) fuzzy systems, when states are not available for measurement of feedback. We present a new approach, which is to design an observer based on fuzzy implications, with fuzzy sets in the antecedents, and an asymptotic observer in the consequents. Each fuzzy rule is responsible for observing the states of a locally linear subsystem. An example illustrates the design procedure.