A Global Exponential Fuzzy Observer Design for Time-Delay Takagi–Sugeno Uncertain Discrete Fuzzy Bilinear Systems With Disturbance

A robust
H
_∞
fuzzy observer is proposed for a class of time-delay Takagi-Sugeno (T-S) uncertain discrete fuzzy bilinear systems with disturbance. Utilizing the Lipschitz conditions and some variable transformations, a linear matrix inequality (LMI) approach is developed, and a sufficient condition is obtained to design the robust
H
_∞
fuzzy observer. The robust
H
_∞
fuzzy observer for time-delay T-S uncertain discrete fuzzy bilinear systems with disturbance can be obtained directly through the LMIs with no preassigned matrices. The convergent rate of the error state can be estimated from the initial conditions and the delay time of T-S uncertain discrete fuzzy bilinear systems. The designed robust
H
_∞
fuzzy observer can guarantee the dynamics of the observer error to be globally exponentially stable and has a prescribed
H
_∞
performance. A numerical example is given to demonstrate the feasibility and effectiveness of the proposed observer design method.