H−/H∞H−/H∞ fault detection filter design for discrete-time Takagi–Sugeno fuzzy system

In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable. The idea is to formulate the robust fault detection observer design as an H−/H∞H−/H∞ problem. Based on nonquadratic Lyapunov functions, a solution of the considered problem is then given via a Linear Matrix Inequality (LMILMI) formulation. An example is proposed to illustrate the design conditions.